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A stability criterion is derived for mode transitions in the discharge current oscillations of a magnetically shielded Hall thruster. The two-equation model evaluated in Paper I for these large-amplitude (> --> 100 % background), low-frequency (< 25 kHz) current oscillations is generalized and then validated with measurements from a 9 kW class test article. It is shown that the model can re-create quantitatively trends in both oscillation amplitude and frequency with discharge voltage and current. The validated model is non-dimensionalized and applied to derive an analytical stability criterion for the onset of large-amplitude oscillations. The resulting expression depends on several properties, including discharge current, discharge voltage, neutral transit time in the channel, length of the acceleration zone, magnetic field strength, and channel area. The criterion is leveraged to inform two mitigation strategies—changing magnetic field strength and controlling anode temperature— for adjusting the stability margin of the thruster. The criterion is also employed to motivate a physical explanation for why mode transitions occur and, in turn, why the stability margin differs between shielded and unshielded thrusters. [ABSTRACT FROM AUTHOR]

Bimetallic, reactive multilayers are uniformly structured materials composed of alternating sputter-deposited layers that may be ignited to produce self-propagating mixing and formation reactions. These nanolaminates are most commonly used as rapid-release heat sources. The specific chemical composition at each metal/metal interface determines the rate of mass transport in a mixing and formation reaction. The inclusion of engineered diffusion barriers at each interface will not only inhibit solid-state mixing but also may impede the self-propagating reactions by introducing instabilities to wavefront morphology. This work examines the effect of adding diffusion barriers on the propagation of reaction waves in Co/Al multilayers. The Co/Al system has been shown to exhibit a reaction propagation instability that is dependent on the bilayer thickness, which allows for the occurrence of unstable modes in otherwise stable designs from the inclusion of diffusion barriers. Based on the known stability criteria in the Co/Al multilayer system, the way in which the inclusion of diffusion barriers changes a multilayer's heat of reaction, thermal conductivity, and material mixing mechanisms can be determined. These factors, in aggregate, lead to changes in the wavefront velocity and stability. [ABSTRACT FROM AUTHOR]

The stability of holes in solid thin films is crucial, as an absence of holes is necessary in some applications and holes are needed in others. We develop an axisymmetric two grain model with a central hole, with surface diffusion governing the exterior surfaces and mean curvature motion governing the grain boundary. The model can exhibit grooving, wetting, dewetting, as well as void, hole, and hillock formation. Here, we extend an earlier work [Zigelman and Novick-Cohen, J. Appl. Phys. 130, 175301 (2021)], where it was shown for an axisymmetric single grain system with a hole at the center that there exists a critical effective radius, which is independent of the contact angle. The stability of the steady states, which consist of coupled nodoidal and catenoidal surfaces, is analyzed numerically by imposing the steady state configurations as initial conditions. This approach yields stability criteria in terms of (i) the effective energy, (ii) the ratio between the maximal thickness of the inner and outer grains, (iii) a generalized effective radius, and (iv) the ratio between the mean curvature of the exterior surfaces and the total volume of the system. Some of these criteria partially reflect the Rayleigh stability criterion. Hillock formation tends to be stabilizing. Modes of instability include growth of one grain at the expense of the other, breakup induced by grooving, and hole closure. [ABSTRACT FROM AUTHOR]

We derive a precise energy stability criterion for smooth periodic waves in the Degasperis–Procesi (DP) equation. Compared to the Camassa-Holm (CH) equation, the number of negative eigenvalues of an associated Hessian operator changes in the existence region of smooth periodic waves. We utilize properties of the period function with respect to two parameters in order to obtain a smooth existence curve for the family of smooth periodic waves with a fixed period. The energy stability condition is derived on parts of this existence curve, which correspond to either one or two negative eigenvalues of the Hessian operator. We show numerically that the energy stability condition is satisfied on either part of the curve and prove analytically that it holds in a neighborhood of the boundary of the existence region of smooth periodic waves. [ABSTRACT FROM AUTHOR]

In this paper we study the permanence and impermanence for continuous-time competitive Kolmogorov systems via the carrying simplex. We first give an extension to attractors of V. Hutson's results on the existence of repellors in continuous-time dynamical systems that have found wide use in the study of permanence via average Liapunov functions. We then give a general criterion for the stability of the boundary of carrying simplex for competitive Kolmogorov systems of differential equations, which determines the permanence and impermanence of such systems. Based on the criterion, we present a complete classification of the permanence and impermanence in terms of inequalities on parameters for all three-dimensional competitive systems which have linearly determined nullclines. The results are applied to many classical models in population dynamics including the Lotka-Volterra system, Gompertz system, Leslie-Gower system and Ricker system. [ABSTRACT FROM AUTHOR]

This article explores the criteria for fixed‐time stability (FxTS) within nonlinear impulsive dynamical systems, encompassing both stabilizing and destabilizing impulses. Initially, employing the Lyapunov method, the article delineates a criterion for FxTS, particularly when impulsive sequences are delineated by an average impulsive interval. Following this, the article innovatively applies two integral inequalities to introduce an optimized criterion for uniform impulsive sequences, evidencing its lesser conservativeness relative to the initial criterion. Moreover, this article derives a necessary condition for dynamical systems subjected to destabilizing impulses. Intriguingly, the investigation reveals the existence of a minimal threshold for the maximum impulsive interval, below which the system cannot achieve FxTS. This result elucidates why existing literature uniformly imposes a specific condition on the impulsive interval for destabilizing impulses. Finally, the efficacy of the proposed theory is underscored through numerical examples. [ABSTRACT FROM AUTHOR]

In this manuscript, a general geometric singular perturbation framework to study pattern formations in nonlinear reaction-diffusion (R-D) systems with single or multiple strong localized impurities is developed. In the method, we divide the spatial domain into fast and slow regions respectively near and far away from the positions of impurities. In each region, the limiting fast or slow system is defined separately in terms of different scales. By so doing, the R-D system with strong localized impurities can be transformed into a singularly perturbed problem with suitable slow-fast structure. We then solve the limiting fast and slow flow explicitly and matching them approximately. Accordingly, the existence and stability criterion on the pinned 1-pulse and multiple-pulse solutions can be set up analytically. Numerical simulations are also performed to verify the theoretical predictions. [ABSTRACT FROM AUTHOR]

This study focused on the equation of motion, hydrodynamic derivatives, and course stability with respect to ship maneuvering in a canal. Based on the potential theory, a consistent linearized equation of motion was derived when a ship maneuvers near the center line of a canal with a symmetrical cross-section and uniform length. In the new equation of motion, hydrodynamic derivatives for the lateral force and yaw moment with respect to ship heading angle ψ ( Y ψ , N ψ ) appear, which have not been considered in existing studies. Y ψ and N ψ are measured by captive tests using a container ship model in a canal model, and they are significant. Furthermore, the course stability criterion for ships in the canal was derived by considering the Y ψ and N ψ , and the course stability was investigated. As a result, we found that the effect of Y ψ and N ψ on course stability cannot be neglected when the water depth becomes shallower. In case of the studied container ship, the consideration of Y ψ and N ψ causes the ship to shift to the course stable direction. [ABSTRACT FROM AUTHOR]

In the realm of discrete-time modeling for gene regulatory networks, significant focus has been placed on addressing the time lags inherent in the process of DNA transcription to RNA and the subsequent translation of mRNA to proteins. These temporal delays have been consistently incorporated into discrete gene regulatory network models. However, true gene regulatory networks are also subject to spatial variables, due to the uneven distribution of protein and mRNA concentrations. The integration of reaction-diffusion terms is thus essential to fully represent the impact of spatial dynamics on gene regulatory networks. In such networks, reaction-diffusion dynamics highlight the complex interactions between neighboring spatial regions, where closeness leads to mutual influences on their functional activities. Based on this conceptual groundwork, this study introduces a discrete-time gene regulatory network model that includes the mutual interconnections between spatial areas. To guarantee the model's robust stability, we have established delay-dependent stability criteria using carefully designed Lyapunov-Krasovskii functions, framed within the context of linear matrix inequalities. The robustness and effectiveness of our approach are demonstrated through a numerical example presented in this work. [ABSTRACT FROM AUTHOR]

In this paper, we pay attention to event-based iterative learning predictive control for the iterative learning system affected by network delays under two-dimensional (2D) framework. First, the well-posed iterative learning predictive system is introduced to depict the lost data induced by network delays. Subsequently, the prediction-batch–based event-triggered protocol is formulated to help alleviate the adverse influence of network delays. Based on these preparations, we attempt to solve iterative learning predictive control by virtue of the 2D system theorem. To this end, the 2D Roesser-type predictive control model is carried out to describe the iterative learning predictive system, and then, the predictive control problem is considered for such 2D Roesser predictive model. The corresponding stability criteria and controller design are achieved, which also realize the tracking control of the iterative learning system. To conclude this paper, the examples are examined to illustrate the effectiveness of the proposed approach and controller design. [ABSTRACT FROM AUTHOR]

This paper studies the stability of discrete-time time-varying stochastic systems with infinite Markov switching. First, the concepts of strongly exponentially stable in mean square and exponentially stable in mean square with conditions are introduced, and their equivalent conditions are given by operator theory and stochastic analysis. Second, we introduce the Lyapunov equation related to strongly exponentially stable in mean square. Third, as an application of the proposed Lyapunov stability criterion, the relationship between the internal stability and the l 2 input–output state stability is derived for the infinite Markov jump system disturbed by finite-energy random disturbance. Finally, an example is given to verify its correctness and validity. [ABSTRACT FROM AUTHOR]

This article studies the finite time stability (FNTS) of time-varying nonlinear stochastic systems with random impulses. We provide sufficient conditions for the FNTS or even fixed time stability (FXTS) for time-varying stochastic systems under two cases: (1) The impulse time is deterministic; (2) The impulse time is random. For case (1), we use the reverse average dwell time to investigate FNTS, but for case (2), we employ the Poisson process theory to solve the stability problem. In addition, the stability criteria capture the stabilising effect of stochastic noise in the FNTS problem. Finally, the correctness of the theoretical results is verified with two numerical examples. As far as the author knows, no one has studied the FNTS of time-varying stochastic systems with random impulses. [ABSTRACT FROM AUTHOR]

This paper presents an adaptive probabilistic recurrent Takagi-Sugeno-Kang fuzzy neural PID controller for handling the problems of uncertainties in nonlinear systems. The proposed controller combines probabilistic processing with a Takagi-Sugeno-Kang fuzzy neural system to proficiently address stochastic uncertainties in controlled systems. The stability of the controlled system is ensured through the utilization of Lyapunov function to adjust the controller parameters. By tuning the probability parameters of the controller design, an additional level of control is achieved, leading to enhance the controller performance. Furthermore, it can operate without relying on the system's mathematical model. The proposed control approach is employed in nonlinear dynamical plants and compared to other existing controllers to validate its applicability in engineering domains. Simulation and experimental investigations demonstrate that the proposed controller surpasses alternative controllers in effectively managing external disturbances, random noise, and a broad spectrum of system uncertainties. • We propose an adaptive probabilistic recurrent TSK fuzzy neural PID controller. • The Lyapunov stability criterion is used to update the proposed controller parameters. • The proposed controller is applied practically for controlling a servo motor. [ABSTRACT FROM AUTHOR]

Investigating novel compounds has become necessary due to the need for sophisticated materials in optoelectronic devices and spintronics. Because of their unique properties, magnesium-based spinels MgSm2X4 (X = S and Se) are very promising for these applications. We used the spin-polarized PBEsol for structural properties and the PBEsol functional for mechanical behavior, both using the WIEN2k code. Both compounds' stability in the magnetic and non-magnetic phases was validated by the Birch-Murnaghan equation of state, and their stability in the cubic phase was verified by the Born stability criterion. Their ductile character was shown by the computation of Pugh's ratio and Poisson ratio. Both MgSm2S4 and MgSm2Se4 display metallic behavior in the spin-up channel and semiconducting behavior in the spin-down channel, indicating a half-metallic nature, according to TB-mBJ potential calculations. With total magnetic moments of 20 μB, both materials showed ferromagnetic properties. Samarium ions contributed 5.27 μB for MgSm2S4 and 5.34 μB for MgSm2Se4. Furthermore, we computed optical parameters in the energy range of 0 to 15 eV, such as absorption, extinction coefficient, reflectivity, dielectric function, and refractive index. Our results demonstrate the potential of MgSm2X4 spinels for future technological developments by revealing their prospective optoelectronic and spintronic applications. [ABSTRACT FROM AUTHOR]

This paper mainly concerns on the tracking control problem for event‐triggered networked control systems (NCSs) with diversified cyber‐attacks. An event‐triggered mechanism (ETM) is exploited to decrease the amount of redundant transmissions, thus saving communication resources. In addition, a novel tracking error model for NCSs is built with consideration of ETM and diversified cyber‐attacks, which involves deception attacks and Denial‐of‐Service (DoS) attacks. On the basis of Lyapunov stability theory and linear matrix inequalities (LMIs), the stability criterion of the tracking error system is constructed, and the controller is designed to ensure the tracking performance of the system. In the end, simulation examples are provided to testify the validity of the proposed method. [ABSTRACT FROM AUTHOR]

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In this paper, we have developed a class of new solutions for relativistic compact stars in higher-dimensional (D ≥ 4) space-time assuming pseudo-spheroidal geometry of the grr metric component. To study the physical properties, we consider equation of state of interior strange matter p = 1 3(ρ − 4B), as proposed in MIT bag model in the presence of a density-dependent B parameter. The interior matter of a quark star may consist of three flavor quarks. We observe some interesting results. The parameter B depends on the anisotropy (α) in the interior, and at the stellar surface, B attains a constant value independent of α. At the interior, B increases with the increase of α. We also note that the value of B approaches a constant value with increasing spheroidal parameter λ. B(ρ) also depends on space-time dimensions and it is interesting to note that B(ρ) picks up negative values near core region which limits the number of space-time dimensions available for a stellar model. All the stability criterion and energy conditions hold good for a physically realistic stellar configuration. It is observed that strange quark matter may be stable or metastable or unstable depending upon the value of energy per baryon (EB). Strange quark matter will be stable if energy per baryon EB < 930.4MeV/fm3. It is noted that the maximum mass obtainable in this model is 1.99M⊙ considering stable strange quark matter when dimension D = 4. In addition, we observe that the dimensions have some effect on the gross properties of strange stars (SS). [ABSTRACT FROM AUTHOR]

The pressure dependence of mechanical and electrical properties of AlAs1-xPx is studied within the pressure range of 0–120 kbar using the empirical pseudopotential method (EPM) with virtual crystal approximation (VCA). There is a good agreement between the estimated data and the available experimental measurements. The electronic band gap of AlAs1-xPx under the impact of pressure has been determined. The mechanical stability under the pressures is evaluated by the stability criterion, based on the elastic constants that are determined at various pressures. The values of bulk, shear, and Young's moduli are determined which rise with the rise in pressure. The computed bulk/shear values indicate that the alloys under investigation are ductile. [ABSTRACT FROM AUTHOR]

In order to reduce carbon emissions from the power grid, photovoltaic (PV) generation units and controllable nonlinear loads based on power electronic devices are gradually becoming more prevalent in the power system. In a PV grid-connected system featuring controllable nonlinear loads, the interplay among PV grid-connected inverters, the loads, and the grid can potentially lead to voltage oscillations. To tackle this challenge, this paper introduces an optimization-based method for suppressing oscillations, which carefully balances system stability with response performance. Firstly, an impedance model of the system is established by applying the harmonic linearization method, and system stability is analyzed using the "logarithmic frequency stability criterion". Subsequently, impedance relative sensitivity is used to identify key parameters that affect system stability, and the interaction between key parameters is considered to analyze the stability range for these parameters. On this basis, a parameter optimization method based on the particle swarm optimization algorithm is proposed to balance system stability and response performance. The effectiveness and robustness of this method are verified through a simulation analysis. [ABSTRACT FROM AUTHOR]

The problem of optimal synthesis of a nonlinear system's control law parameters of satellite attitude control under constraints is considered. The maximum stability degree of a system is considered as an optimality criterion. The reaction wheels' control moments and angular velocities achievable within the drives' physical characteristics are considered as constraints. A linear model of the system converted from the original nonlinear model was used to solve the problem. The decomposition method, based on the transition from real time to relative time, is used to separate the tasks of optimality criterion maximization and constraints consideration. A method of synthesizing the optimal form of system transient process according to the maximum stability degree criterion is developed. An analytical method for determining the optimal values of control law parameters is proposed, based on the structural features of the linear differential equations system. A method that takes into account constraints on control moments and angular velocities of reaction wheels, based on transition scale from relative time to real time and its calculation algorithm, ensuring that conditions of all constraints are met, is developed. An example of solving the problem of optimal system synthesis is considered. The results demonstrate the effectiveness and simplicity of the proposed methods and algorithm for targeted selection of a system's technical characteristics, taking into account constraints on reaction wheels' maximum angular velocities and control moments values. [ABSTRACT FROM AUTHOR]

The global stability of a nonautonomous 3-species ratio-dependent diffusive predator-prey model is studied in this paper. Firstly, some easily verifiable sufficient conditions which guarantee the existence of the strictly positive space homogenous periodic solution (SHPS) of the ratio- dependent predator-prey model (RDPPM) with diffusive and variable coefficient are achieved by using a comparison theorem of differential equation and fixed point theorem. At the same time, some new analysis techniques are developed as a byproduct. Secondly, some sufficient conditions ensuring the globally asymptotically stability of the strictly positive SHPS of the diffusive nonautonomous predator-prey model are given by using the method of upper and lower solutions (UALS) for the parabolic partial differential equations and Lyapunov stability theory. In addition, two numerical examples are given to validate the theoretical results obtained in this paper. [ABSTRACT FROM AUTHOR]

This article addresses the problem of dynamic event‐triggered asynchronous output feedback controller design for discrete‐time switched systems under deception attacks. To conserve communication resources and restrict asynchronous time, a dynamic event‐triggered mechanism is established which permits the system to switch many times in the trigger interval. Then, stability criteria for the underlying system despite the impact of deception attacks are obtained via the Lyapunov function and average dwell time method. Meanwhile, a co‐design scheme for dynamic output feedback gains and dynamic event‐triggered parameters are provided. Finally, two simulations are used to demonstrate the effectiveness of the approach. [ABSTRACT FROM AUTHOR]

To address the challenges in establishing the state transfer matrix and the complexity of eigenvalue calculation in determining the multi-parameter stability boundaries of high-order nonlinear Vienna rectifiers, a novel numerical computation method is proposed in this paper. This method leverages a numerical stability criterion and a grid variable step search to efficiently calculate these stability boundaries. The small-signal model of the Vienna rectifier is derived by constructing the time-varying state transfer matrix using the periodic solution of the harmonic balance method. Eigenvalues are rapidly calculated via the periodic numerical solution of the state transfer matrix. The proposed parameter sensitivity-based grid variable step search method ensures a fast and accurate determination of stability boundaries. A hardware experimental setup is established to validate the stability boundaries of the Vienna rectifier under various parameter variations, including load, component, and control changes. The experimental results closely match the simulations, confirming the correctness and superiority of the proposed method. [ABSTRACT FROM AUTHOR]

In recent years, alcohol addiction has become a major public health concern and a global threat due to its potential negative health and social impacts. Beyond the health consequences, the detrimental consumption of alcohol results in substantial social and economic burdens on both individuals and society as a whole. Therefore, a proper understanding and effective control of the spread of alcohol addictive behavior has become an appealing global issue to be solved. In this study, we develop a new mathematical model of alcohol addiction with treatment class. We analyze the dynamics of the alcohol addiction model for the first time using advanced operators known as fractal–fractional operators, which incorporate two distinct fractal and fractional orders with the well-known Caputo derivative based on power law kernels. The existence and uniqueness of the newly developed fractal–fractional alcohol addiction model are shown using the Picard–Lindelöf and fixed point theories. Initially, a comprehensive qualitative analysis of the alcohol addiction fractional model is presented. The possible equilibria of the model and the threshold parameter called the reproduction number are evaluated theoretically and numerically. The boundedness and biologically feasible region for the model are derived. To assess the stability of the proposed model, the Ulam–Hyers coupled with the Ulam–Hyers–Rassias stability criteria are employed. Moreover, utilizing effecting numerical schemes, the models are solved numerically and a detailed simulation and discussion are presented. The model global dynamics are shown graphically for various values of fractional and fractal dimensions. The present study aims to provide valuable insights for the understanding the dynamics and control of alcohol addiction within a community. [ABSTRACT FROM AUTHOR]

This article investigates the adaptive tracking control problem for switched nonlinear systems with input quantization and hysteresis nonlinearity. First, the hysteresis nonlinear phenomenon is considered and the Bouc–Wen hysteresis model is employed to address the complexities of controller design. Considering the time‐sampling mechanism may lead to the wastage of communication resources, a hysteresis quantizer is introduced to address this issue. Additionally, a command filter is constructed to relieve complexity explosion issues encountered during the backstepping process. Subsequently, compared with the conventional predefined‐time lemma, a novel predefined‐time lemma is proposed which can effectively adjust system performance even if the predefined‐time parameter is determined. In this case, a novel adaptive predefined‐time control scheme is devised by considering hysteresis properties and input quantization via the application of backstepping, which can track the reference signals within the predefined‐time frame. Finally, the flexibility and effectiveness of the proposed strategy are elaborated through numerical and practical examples. [ABSTRACT FROM AUTHOR]

This study presents a reliable mathematical model to explain the spread of typhoid fever, covering stages of susceptibility, infection, carrying, and recovery, specifically in the Sheno town community. A detailed analysis is done to ensure the solutions are positive, stay within certain limits, and are stable for both situations where the disease is absent and where it is consistently present. The Routh-Hurwitz stability criterion has been used and applied for the purpose of stability analysis. Using the next-generation matrix, we determined the intrinsic potential for disease transmission. It showing that typhoid fever is spreading actively in Sheno town, with cases above a critical level. Our findings reveal the instability of the disease-free equilibrium point alongside the stability of the endemic equilibrium point. We identified two pivotal factors for transmission of the disease: the infectious rate, representing the speed of disease transmission, and the recruitment rate, indicating the rate at which new individuals enter the susceptible population. These parameters are indispensable for devising effective control measures. It is imperative to keep these parameters below specific thresholds to maintain a basic reproduction number favorable for disease control. Additionally, the study carefully examines how different factors affect the spread of typhoid fever, giving a detailed understanding of its dynamics. At the end, this study provides valuable insights and specific strategies for managing the disease in the Sheno town community. [ABSTRACT FROM AUTHOR]

Aiming at the solid oxide fuel cell (SOFC) applied to the ship DC microgrid in the face of pulse load disturbance is prone to make the SOFC voltage drop too large leading to the DC grid oscillation problem. In this paper, a stability criterion method for SOFC-Li battery DC system based on hybrid potential function is proposed. Firstly, a mathematical model of shipboard DC microgrid with SOFC-Li battery is established and the accuracy of the model is verified. Then, the stability criterion of the system based on the hybrid potential function under large disturbances is constructed. Subsequently, the effects of system stability under impulse load conditions were analysed under different parameters. Based on the constructed criterion, simulation verification of the stability boundary conditions of the SOFC system operating independently or jointly with a lithium battery system is carried out. The experimental results show that the proposed stability criterion and control strategy are effective in accurately predicting the system stability boundary. The experimental results verify the effectiveness of the proposed method in improving the stability of the system and provide a theoretical basis for further research on the dynamic characteristics of SOFC systems under complex load conditions. [ABSTRACT FROM AUTHOR]

Bacterial respiratory tract infections (e.g., in patients with cystic fibrosis) may be treated with the intravenous infusion of a piperacillin/tazobactam (P/T) solution through an elastomeric device. In the present work, we combined a 24-h drug stability study with an assessment of the drug solution flow rate during an in vitro simulated infusion. Experiments were performed in triplicate with two excipient-free generic P/T solutions and an excipient-containing proprietary P/T solution in saline (all 50/6.25 mg/mL) released from an elastomeric infusion device at 32 °C. The P/T solutions' stability was assessed by an HPLC-UV assay, pH and osmolality measurements, a visual assessment, and particle counting. Before these analyses, a forced degradation study was performed. To assess the flow rate, a precision scale was used to weigh the solution collected at the infusion line outlet. The stability criteria were <10% degradation and a flow rate within ± 15% of the nominal value over the 24-h infusion period: all three P/T solutions were found to be stable. The actual flow rate was lower than the expected flow rate; this difference was probably due to the drug solution's high viscosity and must be taken into account in clinical use. [ABSTRACT FROM AUTHOR]

Descriptor systems are more complex than normal systems, which are modeled by differential equations. This paper derives stability and stabilization criteria for uncertain fractional descriptor systems with neutral-type delay. Through the Lyapunov–Krasovskii functional approach, conditions subject to time-varying delay and parametric uncertainty are formulated as linear matrix inequalities. Based on the established criteria, static state- and output-feedback control laws are designed to ensure regularity and impulse-free properties, together with robust stability of the closed-loop system under permissible uncertainties. Numerical examples illustrate the effectiveness of the control methods and show that the results depend on the range of variation in the delays and on the fractional order, leading to stability analysis results that are less conservative than those reported in the literature. [ABSTRACT FROM AUTHOR]

In this paper, the state observer for coupled cyclic genetic regulatory networks with time delays is designed. The coupling network is composed of two cyclic genetic subnets, which inhibit each other directly. By constructing a suitable Lyapunov – Krasovskii functional velated to the eyclic struction, the delay-dependent stability criteria of the error system are investigated in the form of linear matrix inequalities. Thereby, the state observer of the considered genetic regulatory networks is obtained. Finally, two numerical examples are given to illustrate the effectiveness of the theoretical results. [ABSTRACT FROM AUTHOR]

This paper is dedicated to investigating the chaos of a initial-boundary value (IBV) problem of a multi-dimensional weakly hyperbolic equation subject to two general nonlinear boundary conditions (NBCs). The existence and uniqueness of solution for the IBV problem are established. By employing the snap-back repeller and heteroclinic cycle theories, it has been proven that the IBV problem with a linear and a general NBCs exhibits chaos in the sense of both Devaney and Li–Yorke. Furthermore, these chaotic results are extended to the IBV problem with two general NBCs. Two stability criteria of the IBV problem are established, respectively, for the corresponding two cases of boundary conditions. Finally, numerical simulations are presented to illustrate the theoretical results. [ABSTRACT FROM AUTHOR]

• Memory sampled-data control is applied for the uncertain rigid spacecraft model. • Randomly missing measurement in the system output obeys the Bernoulli distribution. • It tolerates uncertainty and disturbances using the H ∞ technique. • A novel looped and delay-dependent LKF is constructed for the proposed systems. • It gives the minimum disturbance attenuation level compared with existing works. This paper focuses on stabilizing the attitude of the rigid spacecraft under the sampled-data control design technique with constant communication delay. The system dynamics with model uncertainty (perturbation) and missing measurements are considered. The aim is to design a desirable attitude control that ensures the stabilization of the rigid spacecraft with an optimal H ∞ performance level. A novel Lyapunov–Krasovskii functional is developed, incorporating looped characteristics, for the proposed study on the rigid spacecraft model by developing relevant new terms. Making use of the Lyapunov function as well as free-matrix-based integral inequality, sufficient stability criteria are established to assure the stability of the rigid spacecraft model. Furthermore, the desired sampled-data control gain matrices are acquired through the solution of linear matrix inequalities, which guarantees the asymptotic stability of the rigid spacecraft model. Finally, the numerical simulation demonstrates the efficacy of the theoretical study proposed for the rigid spacecraft model. [ABSTRACT FROM AUTHOR]

Introduction: Cariprazine treats acute manic and depressive episodes in bipolar I disorder (BP‐I), but its efficacy in preventing relapse of mood episode remains unknown. Methods: In this phase 3b, double‐blind, placebo‐controlled study, patients with BP‐I with acute manic or depressive episodes (each with/without mixed features), were treated with cariprazine 3.0 mg/day during a 16‐week open‐label treatment period; those who achieved stable remission within 8 weeks and remained stable for at least another 8 weeks were randomized to receive cariprazine 1.5 or 3.0 mg per day or placebo in the double‐blind treatment period for up to 39 weeks. The primary efficacy endpoint was time to relapse of any mood episode. Adverse events (AEs) were assessed. Results: Patients (440/896) enrolled in the open‐label treatment period achieved stability criteria and were randomized to receive cariprazine 3.0 mg/day (n = 148), cariprazine 1.5 mg/day (n = 147), or placebo (n = 145) in the double‐blind treatment period. Relapse rates were 17.9%, 16.8%, and 19.7% in the cariprazine 3.0 mg/day, cariprazine 1.5 mg/day, and placebo groups, respectively. Neither dose of cariprazine was more effective than placebo on the primary outcome (3.0 mg/day: HR = 0.89, [95% CI: 0.5, 1.5]; 1.5 mg/day: HR = 0.83, 95% CI [0.5, 1.4]). The most frequently reported AEs (≥5%) were akathisia, headache, insomnia, and nausea in the open‐label treatment period and increased weight and insomnia in the double‐blind treatment period. In the open‐label and double‐blind treatment periods, 7.5% and 1.6% of patients experienced an AE leading to discontinuation. Conclusion: Cariprazine was not superior to placebo in the prevention of relapses in this study. Relapse rates were unusually low in the placebo group. Cariprazine was well‐tolerated. [ABSTRACT FROM AUTHOR]

This paper describes a new approach to control stall and surge instabilities in the compressor system by using of finite time backstepping-based adaptive sliding mode method. The most important innovation of this study is to provide a finite time adaptive control method to simultaneously prevent the stall and surge instabilities in a compressor system in the presence of disturbance and uncertainty in the compressor characteristic curve as well as the throttle valve. The disturbance and uncertainty issues are covered by a robust sliding mode control and the gain coefficients of this controller as well as the estimation of uncertain terms are obtained by using the adaptive method. The Lyapunov stability criterion is used to evaluate the finite-time stability of the closed-loop system. The performance of the proposed method is compared with other literature methods through simulation in Matlab. The simulation results show that the proposed controller is better than the existing methods in terms of surge preventing and robustness against uncertainty and disturbance. [ABSTRACT FROM AUTHOR]

This paper proposes an observer-based hierarchical distributed model predictive control (MPC) strategy for ensuring speed consistency in multi-linear motor traction systems. First, a communication topology is considered to ensure information exchange. Secondly, the control architecture of each agent is divided into upper layers and lower layers. The upper layer utilizes a distributed MPC method to track the leader's speed. The lower layer uses a decentralized MPC method to track the command signals sent by its upper layer controller. In addition, to eliminate the negative impact of disturbance, a nonlinear disturbance observer is designed. We then prove the asymptotic stability of the entire system by properly designing the Lyapunov equation. Finally, the feasibility of the proposed strategy is verified based on several simulations. • A hierarchical distributed model predictive control for multi-linear motor traction systems is introduced. • The nonlinear disturbance observers are adopted to improve the system's robustness. • A strict proof is constructed for the Lyapunov criterion of asymptotic stability. [ABSTRACT FROM AUTHOR]

This paper aims to analyze the stability of a special class of single-channel slow-rotating homing missiles using the Frank–Wall stability criterion. To achieve this, starting from the model of a slow-rolling missile with six degrees of freedom (6 DOFs) in the body frame, a 6-DOFs model in the Resal frame is obtained, which is used to linearize the coupled commanded motion. Based on the linearized model, we obtain the structural scheme of the commanded object and define the flight quality parameters. The obtained linear model has a complex representation (with real and imaginary parts) due to the coupling between longitudinal channels for the rolling missile. Then, the kinematic guidance equations, the seeker equations and the actuator relations using a switching function, specific to the slow-rolling single-channel missile, are defined. The guidance kinematic equations, the seeker equations and the actuator model are linearized in the Resal frame, and the structural diagram of the homing missile is constructed. Starting from this, the characteristic polynomial having complex coefficients is determined and then analyzed with the Frank–Wall stability criterion. Based on the analysis, a stability range is determined for the navigation constant (k) , and a minimum and possibly a maximum limit for the time to hit the target t g o is obtained. The stability range defined for the navigation constant in the linear model is finally validated in the nonlinear model in the body frame. [ABSTRACT FROM AUTHOR]

To predict the potential success of an invading non-native species, it is important to understand its dynamics and interactions with native species in the early stages of its invasion. In spatially implicit models, mathematical stability criteria are commonly used to predict whether an invading population grows in number in an early time period. But spatial context is important for real invasions as an invading population may first occur as a small number of individuals scatter spatially. The invasion dynamics are therefore not describable in terms of population level state variables. A better approach is spatially explicit individual-based modeling (IBM). We use an established spatially explicit IBM to predict the invasion of the non-native tree, Melaleuca quinquenervia (Cav.) Blake, to a native community in southern Florida. We show that the initial spatial distribution, both the spatial density of individuals and the area they cover, affects its success in growing numerically and spreading. The formation of a cluster of a sufficient number and density of individuals may be needed for the invader to locally outcompete the native species and become established. Different initial densities, identical in number and density but differing in random positions of individuals, can produce very different trajectories of the invading population through time, even affecting invasion success and failure. [ABSTRACT FROM AUTHOR]

A zone control algorithm is proposed that considers both economic performance indicators and control performance indicators. Unlike classic set point control, zone control expands the control target into a convex set. In this study, an ellipsoid is used as the control target, and the advantages of the ellipsoid target are explained in terms of overall stability and computational load. After defining the distance measurement function and appropriate terminal constraints, an objective function that considers both control performance and optimization performance is constructed. A theoretical analysis shows that the proposed control algorithm satisfies the Lyapunov stability criterion. The superiority of the ellipsoid control target in handling complex multivariable control tasks is also demonstrated. This method has significant potential value in practical industrial applications, helping to unleash the potential control performance and economic benefits of zone control systems. Finally, the feasibility and stability of the algorithm are verified through a typical chemical process simulation. [ABSTRACT FROM AUTHOR]

In several applications, the accuracy and robust performance of the control method for the speed of permanent magnet synchronous motors (PMSMs) is critical. Model uncertainties, caused by inaccurate model identification, decrease the accuracy of PMSM control. To solve this problem, this paper presents a super robust control structure for the speed control of PMSMs. In the proposed method, the model uncertainties with Lipschitz condition together with disturbances are considered during the PMSM modeling, and their effects are handled using a robust state feedback control. To be more specific, the Lyapunov stability proof is performed in such a way that the model uncertainty effects are eliminated. Before that, the Lyapunov stability criteria have been selected in such a way that the Hꝏ conditions are considered and guaranteed. This issue helps to eliminate the effects of the disturbances. In addition, this paper considers another option to make the whole control structure robust against sudden load changes. To solve this problem, a fuzzy adaptive sliding mode observer (FASMO) is presented to determine the load torque and use it in the control signal generation. In this observer, the switched gain of the sliding mode observer (SMO) is adapted using a fuzzy system to eliminate the chattering phenomena and increase the estimation accuracy. In fact, the proposed method is called super robust because it resists model uncertainties, disturbances, and sudden load changes during three stages by robust state feedback control, Hꝏ criterion, and load estimator, respectively. The performance of the proposed approach is validated through a set of laboratory tests, and its superiority is shown compared to other methods. [ABSTRACT FROM AUTHOR]

To meet the strong coupling characteristics of the MSCSG deflection channel and the demand for high control accuracy, a two-degree-of-freedom deflection channel model is firstly established for the structure and working principle of the MSCSG; to meet the strong coupling between the two channels, the inverse system method is used to decouple the model; then, the operation principle of the MSCSG system is introduced, and the modeling of the power amplifier is carried out; to meet the demand for high-precision control of the MSCSG rotor system, the RBF neural network is improved using the fuzzy method to achieve high-precision estimation of the residual coupling terms and deterministic disturbances, and the adaptive sliding mode controller is designed. For the high-precision control of the MSCSG rotor system, the fuzzy method is used to improve the RBF neural network to realize the high-precision estimation of the residual coupling term and uncertain perturbation, and the adaptive sliding mode controller is designed, and the convergence of the controller is proved on the basis of the Lyapunov stability criterion. Simulation analysis shows that the method has a large improvement in decoupling performance and anti-disturbance performance compared with the traditional method, and finally, the experiment verifies the effectiveness of the present method and achieves the optimization of the deflection channel controller. The method can be extended to other magnetic levitation actuators and related fields. [ABSTRACT FROM AUTHOR]

We investigate the existence and stability of traveling waves for the sixth‐order Boussinesq equation, considering a broad class of nonlinearities adhering to power‐like scaling relations. Employing the Nehari manifold method, we establish the existence of traveling waves and derive variational criteria for assessing their stability or instability. Subsequently, we develop a numerical approach based on these variational principles to delineate regions of stability and instability. Finally, for homogeneous nonlinearities, we establish a sufficient condition for strong instability. [ABSTRACT FROM AUTHOR]

The mechanical, electronic structure, and optical properties of lithium‐based perovskite LiMgX3 (X = Cl, Br, I) are investigated for the first time at 0–20 GPa using density‐functional theory. The Born stability criteria reveal that the phase transition points of LiMgCl3, LiMgBr3, and LiMgI3 are 20.7, 20.9, and 23.4 GPa, respectively. At 0 GPa, studies on the electronic properties using the Heyd‐Scuseria‐Ernzerhof (HSE06) functional show that LiMgCl3 and LiMgBr3 are indirect bandgap insulators with values of 5.336 and 4.113 eV, whereas LiMgI3 is an indirect bandgap semiconductor with a value of 2.055 eV. In addition, the bandgap calculated using both the PBEsol and HSE06 functionals decreases with increasing pressure, and the bandgap trends with pressure are consistent. Both functionals are also used to study the optical properties of LiMgX3 compounds, which show that they have potential for use in vacuum ultraviolet and photovoltaic applications. The mechanical and optical characteristics of the materials are significantly enhanced under pressure. [ABSTRACT FROM AUTHOR]

This paper is devoted to investigating the behavior of charged compact stars in the f(R,ϕ,X) theory of gravity, where R denotes the Ricci Scalar, ϕ is a scalar potential, and X is a kinetic term. For this purpose, we consider spherically symmetric spacetime with Bardeen geometry as exterior spacetime to investigate various properties of compact stars, including energy density and pressure components. Matching conditions are used to find model parameters. We present a detailed analysis, including a discussion of equations of state parameters, and stability criteria. In this analysis, we discuss the energy conditions to check the viability of our model. Furthermore, an equilibrium condition can be visualized through the modified Tolman–Oppenheimer–Volkov equation. It is concluded that Bardeen’s geometry supports the existence of compact stars in the background of the f(R,ϕ,X) theory of gravity. [ABSTRACT FROM AUTHOR]

Different from the Mittag–Leffler stability or asymptotic stability, the exponential stability issue, which provides faster and explicit convergence rate, is studied in this paper for fractional‐order uncertain systems with asynchronous switching and impulses, where the impulsive functions rely on not only switching modes but also impulsive time. Instead of using the inequality Eα(t)≤1αexp(t1α)(0<α<1)$$ {E}_{\alpha }(t)\le \frac{1}{\alpha}\exp \left({t}^{\frac{1}{\alpha }}\right)\kern0.3em \left(0<\alpha <1\right) $$, by utilizing the theory of fractional‐order differential equations, the methods of Lyapunov function and mathematical induction, some novel and less‐conservative stability criteria are developed, respectively, for the case of switched stable subsystems or switched unstable subsystems. The obtained results build a tradeoff between impulsive function, impulsive interval, average dwell time and fractional order. In addition, our results with α=1$$ \alpha =1 $$ are also novel in contrast with the ones of integer‐order switched impulsive systems. Finally, five numerical examples are given to show the effectiveness of theoretical results. [ABSTRACT FROM AUTHOR]

The small-signal stability of high voltage direct current (HVDC)-connected wind farms (WFs) is a challenging issue in modern power systems. The relative stability, i.e., the stability margin, of such a typical multiple-input multiple-output (MIMO) system is quite difficult to be quantified. This paper evaluates the relative stability of HVDC-connected WFs using a new stability index based on the ν-gap metric. We first develop a MIMO model represented by a transfer function matrix of the HVDC-connected WFs. Then, a new stability index, i.e., the robust stability margin, based on the ν-gap metric is proposed to quantify the relative stability of such a MIMO system. Finally, we propose a method to compute the stable region of control parameters based on the corresponding stability criterion of ν-gap metric. Case studies are given to demonstrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

The conventional adaptive full-order observer-based speed sensorless control method for induction motor is prone to instability at low-speed region as improper feedback gain matrix and imprecise speed adaptive law are often used. To address these problems, a new feedback gain matrix design approach as well as a new speed adaptive law design technique are proposed in this paper. Firstly, considering that the d-axis current estimation error in the traditional feedback gain matrix design method has a great influence on the stability of the speed estimation algorithm, especially at low speeds, a new feedback gain matrix design method is proposed to minimize the d-axis current estimation error. Secondly, a new speed adaptive law design technique is studied based on the conventional method, which only requires the d-axis and q-axis current estimation error with a weight coefficient to be designed, simplifying the conventional speed adaptive law. Thirdly, the transfer function from the speed observation error to the proposed adaptive error is analyzed by Routh stability criterion theory, and the weight coefficient suitable for full range stable operation is determined by MATLAB software. Fourthly, the stability of the proposed method in this paper is analyzed using the poles distribution maps. Finally, the proposed method is experimentally verified based on a 2.2 kW induction motor experimental platform. The experimental results show that the proposed method can make the induction motor operate steadily at low-speed and zero-speed region with rated load. In addition, the proposed method has better anti-disturbance performance than the existing method. [ABSTRACT FROM AUTHOR]

This work investigates the stability conditions for linear systems with time-varying delays via an augmented Lyapunov–Krasovskii functional (LKF). Two types of augmented LKFs with cross terms in integrals are suggested to improve the stability conditions for interval time-varying linear systems. In this work, the compositions of the LKFs are considered to enhance the feasible region of the stability criterion for linear systems. Mathematical tools such as Wirtinger-based integral inequality (WBII), zero equalities, reciprocally convex approach, and Finsler's lemma are utilized to solve the problem of stability criteria. Two sufficient conditions are derived to guarantee the asymptotic stability of the systems using linear matrix inequality (LMI). First, asymptotic stability criteria are induced by constructing the new augmented LKFs in Theorem 1. Then, simplified LKFs in Corollary 1 are proposed to show the effectiveness of Theorem 1. Second, asymmetric LKFs are shown to reduce the conservatism and the number of decision variables in Theorem 2. Finally, the advantages of the proposed criteria are verified by comparing maximum delay bounds in four examples. Four numerical examples show that the proposed Theorems 1 and 2 obtain less conservative results than existing outcomes. Particularly, Example 2 shows that the asymmetric LKF methods of Theorem 2 can provide larger delay bounds and fewer decision variables than Theorem 1 in some specific systems. [ABSTRACT FROM AUTHOR]

• Active wobble control: New method for spinning satellites using reaction wheels. • Reduced weight: Eliminates balancing processes and additional ballast. • Enhanced robustness: Handles uncertainties and high thrusting disturbances. • Minimized oscillations: Lowers average thrust and spin axis variations. • Hardware validated: Successful testing with air-bearing HIL setup. This paper introduces a novel active nutation/wobble rejection control method for spinning satellites enduring thrusting disturbances and reaction wheel limitations. Our approach employs two tilted reaction wheels in reaction-momentum mode, actively controlling wobble/nutation while enhancing disturbance rejection for dynamically unbalanced satellites. This eliminates the need for balancing processes or additional ballast, reducing system weight. A new wheel arrangement and momentum analysis effectively dampens wobble generated by dynamic imbalances. We prove that increasing wheel angular speed about the spinning axis enhances immunity against transverse disturbances. Unlike existing controllers, our method minimizes average thrust/spin axis oscillation while eliminating undesired rates and wobble. Stability is rigorously established through linearized equations and Routh stability criteria. Validation via air-bearing hardware-in-the-loop (HIL) and Monte Carlo tests demonstrates close agreement between predictions and experimental data, highlighting the controller's robustness against high thrusting disturbances. This work represents a significant contribution by achieving active stabilization of unbalanced spin satellites using onboard reaction wheels, potentially paving the way for wider adoption in future spacecraft designs. [ABSTRACT FROM AUTHOR]

This paper presents an alternative method to solve the control problem of an uncertain nonlinear system in strict-feedback form with a time delay. Instead of using Lyapunov–Krasovskii functionals, ordinary Lyapunov functionals are used to design the controllers. In order to address the completely unknown uncertainties of the system, including the unmodeled dynamics, time-delay nonlinearities, and external disturbances, command filters are applied to reconstruct the estimations of such uncertainties, and the negative feedback of these estimations can be used to reduce the influence of such uncertainties on the system. With the help of the backstepping technique and the Lyapunov stability criterion, it is proved that the system output tracks the target signal with a small error, and contrastive simulation results verify our method's effectiveness. [ABSTRACT FROM AUTHOR]

This article investigates the exponential stability of nonlinear discrete‐time systems with time‐varying state delay and delayed impulses, where the delays in impulses are not fixed. Specifically, the study is separated into two cases: (1) stability of delayed discrete‐time systems with destabilizing delayed impulses, where the time delays in impulses can be flexible and even larger than the length of the impulsive interval; (2) stability of delayed discrete‐time systems with mixed delayed impulses (means stabilizing and destabilizing delayed impulses exist simultaneously), where the time delays in impulses are unfixed between two adjacent impulsive instants. First, the concept of average impulsive delay (AID) is extended to discrete‐time systems with delayed impulses. Then, some Lyapunov‐based exponential stability criteria are provided for delayed discrete‐time systems with delayed impulses, where the impulses satisfy the average impulsive interval (AII) condition and the delays in impulses satisfy the AID condition. For the delayed discrete‐time systems with mixed delayed impulses, the exponential stability criterion is provided by limiting the geometric average of the impulses' strengths. The obtained results can be used to study the delayed discrete‐time systems with some large impulses which may even be unbounded. It's also shown that the delays in impulses can have a stabilizing effect on the stability of delayed discrete‐time systems. Some numerical examples are also provided to illustrate the effectiveness and advantage of the theoretical results. [ABSTRACT FROM AUTHOR]