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In this paper we study the stability of cylinder front waves and the propagation of solutions of a nonlocal Fisher-type model describing the propagation of a population with nonlocal competition among bounded and continuous phenotypic traits. By applying spectral analysis and separation of variables we prove the spectral and local exponential stability of the cylinder waves with the noncritical speeds in some exponentially weighted spaces. By combining the detailed analysis with the spectral expansion and the special construction of sub-supersolutions, we further prove the uniform boundedness of the solutions and the global asymptotic stability of the cylinder waves for more general nonnegative bounded initial data, and prove that the spreading speeds and the asymptotic behavior of the solutions are determined by the decay rates of the initial data. Our results also extend some classical results on the stability of planar waves for Fisher-KPP equation to the nonlocal Fisher model in multi-dimensional cylinder case. [ABSTRACT FROM AUTHOR]

A ship steering control law is designed for a nonlinear maneuvering model whose rudder manipulation is constrained in both magnitude and rate. In our method, the tracking problem of the target heading angle with input constraints is converted into the tracking problem for a strict-feedback system without any input constraints. To derive this system, hyperbolic tangent (tanh ) function and auxiliary variables are introduced to deal with the input constraints. Furthermore, using the feature of the derivative of tanh function, auxiliary systems are successfully derived in the strict-feedback form. The backstepping method is utilized to construct the control input for the resulting cascade system. The proposed steering control law is verified in numerical experiments, and the result shows that the tracking of the target heading angle is successful using the proposed control law. [ABSTRACT FROM AUTHOR]

This paper considers three thermoelastic laminated beam systems with Kelvin-Voigt damping and heat flow described by Fourier's law. First, we show that the system is globally well-posed using the linear operator semigroup approach. The main results are exponential and polynomial stability when the systems are fully and partially damped. We establish the exponential stability of a fully damped system and show the lack of exponential stability for two partially damped systems. Furthermore, we demonstrate its polynomial decay with rate $ t^{-\frac {1}{2}} $ t − 1 2 using frequency domain approach due to Borichev and Tomilov. [ABSTRACT FROM AUTHOR]

This article investigates the exponential H∞$$ {H}_{\infty } $$ control issue of bidirectional associative memory neural network (BAMNN) with unbounded time‐varying delays. A bounded real lemma (BRL) is first established via a direct method, which is on the basis of the solutions of BAMNN. Second, based on the obtained BRL, the state feedback controller is designed to guarantee the global exponential stability of the resulting closed‐loop BAMNN with an H∞$$ {H}_{\infty } $$ performance index. Since no Lyapunov–Krasovskii functionals is constructed in the proposed method, the computation burden and complexity are reduced. Lastly, the effectiveness of the theoretical results is illustrated through two numerical examples. [ABSTRACT FROM AUTHOR]

In this technical note, we investigate the practical exponential stability of a positive switched linear system with impulses and all subsystems unstable. By constructing two types of switched discretized Lyapunov functions, we give some new sufficient conditions such that the system achieves practical exponential stability under mode-dependent range dwell time switching. Following this, we apply these results to the practical consensus of multi-agent system under switching topologies. The mathematical analysis is validated by a set of numerical examples. [ABSTRACT FROM AUTHOR]

We present a novel approach to the exponential stability of switched functional differential equations. Our approach does not involve Lyapunov functions. It is simple and based upon spectral properties of Metzler matrices, a comparison principle and the average dwell-time technique. Consequently, some new explicit criteria for the exponential stability of switched functional differential equations are derived. Some illustrative examples are given. [ABSTRACT FROM AUTHOR]

The aim of this work is to construct and analyze a discretization process that preserves exponential stability at the discrete level for a wave propagation problem with boundary damping when a high-order spectral finite element approximation is used. The main idea is to add a stabilizing term to the wave equation that damps the spurious oscillatory components of the solutions. This term is based on a discrete multiplier analysis that ensures the exponential stability of the semi-discrete problem at any order without compromising the rate of convergence of the discretization strategy. Possible applications of this work concern the solution of boundary control problems or data assimilation problems whose efficiency is based on an exponential stability property of an underlying discrete error system. [ABSTRACT FROM AUTHOR]

In the context of the tadpole graph R$$ \mathcal{R} $$, we examine the damped Schrödinger semigroup e−itd2dx2$$ {e}^{- it\frac{d^2}{d{x}^2}} $$. The first step in our analysis involves a meticulous examination of the spectrum and a suitable decomposition of the resolvent's kernel. By doing so, we establish that the generalized eigenfunctions constitute a Riesz basis of a specific subspace of L2(R)$$ {L}^2\left(\mathcal{R}\right) $$. As a result, we demonstrate that the energy corresponding to the system decays exponentially. [ABSTRACT FROM AUTHOR]

The exponential stability of hybrid event‐triggered singular time‐delay (STD) systems is established in this paper. To ensure their exponential stability, we give sufficient conditions for linear matrix inequalities (LMIs) for STD systems with average impulsive gain. Furthermore, zeno behavior is avoided by carefully designing the settings for event‐triggering conditions. A few numerical examples demonstrate the usefulness of the suggested findings. [ABSTRACT FROM AUTHOR]

This article investigates the asynchronous control for a class of nonlinear switched stochastic delayed systems. In response to this issue, the weighted mode‐dependent average dwell time is first applied to switched stochastic systems as a more general switching signal. In addition, the asynchronous phenomenon is considered to address the mismatch in practical applications, where "mismatch" means the switching of the controllers has a delay to the switching of system modes. Then by selecting new multiple Lyapunov–Krasovskii functionals, sufficient conditions for mean‐square exponential stability and an ℋ∞$$ {\mathscr{H}}_{\infty } $$ performance are derived. Finally, numerical examples are provided to illustrate the effectiveness of the proposed methods. [ABSTRACT FROM AUTHOR]

In this article, the asynchronous control problem of switched linear systems with all unstable modes under denial‐of‐service (DoS) attacks is studied. First, the upper bound of the sampling period, which can be easily calculated based on the scenario where all modes are unstable, is obtained under a periodic sampling control strategy. Second, by constructing an appropriate discrete multiple linear quadratic Lyapunov function, an asynchronous control scheme in the form of linear matrix inequalities is devised. To ensure the stability of switched systems under DoS attacks, a sufficient condition for the total duration and frequency of DoS attacks is established. It is shown that the switched system can tolerate DoS attacks up to a certain limit while maintaining exponential stability, and this result is applicable even when all subsystems are unstable. Finally, numerical examples and a comparative study are presented to demonstrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

ABSTRACT This article focuses on the pth moment exponential stability of discrete‐time Markov switched stochastic systems with state‐dependent delay. By using Razumikhin technique, and stochastic analysis techniques, the state‐dependent delay with randomness due to the randomness of the system state can be addressed. With the help of stationary distribution of Markov switching and multiple Lyapunov–Krasovskii functionals approach, an appropriate switching rule is designed and a novel theorem on discrete‐time Markov switched stochastic systems with state‐dependent delay is established. Different from the previous results, the Markov switched with partially unstable subsystems and the state‐dependent delay with randomness are considered in this article, which brings many differences to the stability analysis of the system compared to traditional stability analysis. Furthermore, an illustrative example is performed to illustrate the effectiveness of the main theory. [ABSTRACT FROM AUTHOR]

In this work, we study the existence, uniqueness and exponential stability of periodic mild solution of the Boussinesq system on the real hyperbolic manifold $ \mathbb {H}^d(\mathbb {R}) $ Hd(R) ( $ d \geqslant 2 $ d⩾2). We consider a couple of Ebin-Marsden's Laplace and Laplace–Beltrami operators associated with the corresponding linear system. Our method is based on the dispersive and smoothing estimates of semigroups generated by Ebin-Marsden's Laplace and Laplace–Beltrami operators. First, we prove the existence and uniqueness of the bounded periodic mild solution for the linear system. Next, using the fixed point arguments, we pass from the linear system framework to the semilinear system framework to establish the existence of the periodic mild solution. Additionally, we prove the unconditional uniqueness of periodic mild solution for the Boussinesq system on hyperbolic manifolds. Finally, we establish the exponential stability of periodic mild solution. [ABSTRACT FROM AUTHOR]

In the current study, we present a stochastic SAIS (unaware susceptible-aware susceptible-infectious-unaware susceptible) epidemic dynamic model on complex networks with multi-weights. The disease dynamic is influenced by random perturbations to the force of the infection rates, as well as awareness rates. To analyze the problem of extinction, we discuss both the stochastic asymptotic stability in the large and almost surely exponential stability of the trivial solution. Then, we get some sufficient conditions, which guarantee the stochastic persistence of infectious disease. Based on the Erdös-Réyni random graph, the numerical simulations are given. These not only validate our conclusions but also obtain else significative results. Both theoretical results and numerical simulations further reflect that improvement of risk awareness and reduction of decay in awareness are highly effective in preventing disease spread. And then, environmental noises play a significant role in disease transmission. [ABSTRACT FROM AUTHOR]

ABSTRACT In this paper, we address the system made by two coupled one‐dimensional Moore–Gibson–Thompson equations u⃛+αü−βu̇xx−γuxx=p(αẇx+ẅx)w⃛+α̂ẅ−β̂ẇxx−γ̂wxx=p̂(α̂u̇x+üx)$$\begin{equation*} \left\{ \def\eqcellsep{&}\begin{array}{l} \dddot{u} + \alpha \ddot{u} - \beta \dot{u}_{xx} - \gamma u_{xx} = p(\alpha \dot{w}_{x} +\ddot{w}_{x}) \\[3pt] \dddot{w} + \hat{\alpha }\ddot{w} - \hat{\beta }\dot{w}_{xx} - \hat{\gamma }w_{xx} = \hat{p}(\hat{\alpha }\dot{u}_{x} +\ddot{u}_{x}) \end{array} \right. \end{equation*}$$arising in the description of thermoviscoelastic materials. Here, α,β,γ,α̂,β̂,γ̂>0$\alpha,\beta,\gamma,\hat{\alpha },\hat{\beta },\hat{\gamma }>0$ while pp̂>0$p\hat{p}>0$. When both the MGT equations lie in the subcritical regime, that is, β−γα>0andβ̂−γ̂α̂>0$$\begin{equation*} \beta - \frac{\gamma }{\alpha }>0 \qquad \text{and} \qquad \hat{\beta }- \frac{\hat{\gamma }}{\hat{\alpha }}>0 \end{equation*}$$we prove that the system generates an exponentially stable solution semigroup. This improves some recent results in the literature, where the exponential stability is attained only within either a stronger condition than subcriticality of both equations, or when α$\alpha$ and α̂$\hat{\alpha }$ are sufficiently close. The key idea is to deduce the exponential stability from that of a related system, made by two coupled equations of the viscoelasticity type. The latter result has also an independent interest. [ABSTRACT FROM AUTHOR]

In this paper, we derive the equations that constitute the nonlinear mathematical model of an extensible thermoelastic Timoshenko system. The nonlinear governing equations are derived by applying the Hamilton principle to full von Kármán equations. The model takes account of the effects of extensibility, where the dissipations are entirely contributed by temperature. Based on the semigroups theory, we establish existence and uniqueness of weak and strong solutions to the derived problem. By using a resolvent criterion, developed by Borichev and Tomilov, we prove the optimality of the polynomial decay rate of the considered problem under the condition (65). Moreover, by an approach based on the Gearhart–Herbst–Prüss–Huang theorem, we show the non‐exponential stability of the same problem; but strongly stable by following a result due to Arendt–Batty. In the absence of additional mechanical dissipations, the system is often not highly stable. By adding a damping frictional function to the first equation of the nonlinear derived model with extensibility and using the multiplier method, we show that the solutions decay exponentially if Equation (85) holds. [ABSTRACT FROM AUTHOR]

This paper focuses on the exponential stability and the resilient state feedback controller design for large‐scale networked control systems under denial‐of‐service attacks. The duration of each denial‐of‐service attack is captured by a logical processor embedded in the controller. The closed‐loop system of periodic sampled‐data control is modelled as an aperiodic sampled‐data control system associated with lower and upper bounds on the duration of the denial‐of‐service attack. Two formal results are demonstrated. The first result is the stability criterion for large‐scale networked control systems under denial‐of‐service attacks obtained by constructing a two‐sided mode‐dependent loop‐based Lyapunov–Krasovskii functional under the action of a prediction‐based controller. The second result presents a criterion based on linear matrix inequalities to design the controller against denial‐of‐service attacks. In particular, iterative algorithms are given for computing the allowable delay upper bound for the system. Finally, the effectiveness of the proposed method is verified by the interconnected power systems of the two areas. [ABSTRACT FROM AUTHOR]

This paper investigates the design of a reduced‐order H∞$H_\infty$ filter for a specific class of switched complex network systems with time‐varying delays. To handle the nonlinear components of the complex network, a T‐S fuzzy model is employed to convert them into a set of linear components. To tackle the issue of heavy network load, a memory‐based adaptive trigger mechanism is proposed. In this study, a reduced‐order H∞$H_\infty$ state estimator is designed using the T‐S fuzzy model. To demonstrate the exponential stability of the error system, a suitable Lyapunov function is constructed based on the Lyapunov stability principle. The parameter matrix of the reduced‐order estimator is determined using the linear matrix inequality and convex linearization method. Additionally, a sufficient condition for the exponential stability of the error system at the suppression level is provided. Finally, the feasibility of the proposed scheme is validated through a simulation experiment. [ABSTRACT FROM AUTHOR]

We consider a class of stochastic fuzzy delayed Cohen-Grossberg neural networks without global Lipschitz condition. Based on local Lipschitz condition, we prove the solutions of the given neural networks exist globally and are mean-square exponentially input-to-state stable. Moreover, we highlight the advantages of our novel results by comparing with the results in Zhu and Li (2012) as well as a numerical example. [ABSTRACT FROM AUTHOR]

In this study, a class of neutral-type Rayleigh equations incorporating $$D$$ D operators and $$T$$ T -periodic time-varying coefficients are introduced. By utilising differential inequality techniques, some new sufficient criteria are derived to guarantee the existence and global exponential stability of $$T$$ T -periodic solutions for the addressed equations. Through numerical experiments, the validity of the main findings is verified. [ABSTRACT FROM AUTHOR]

By applying some novel inequality techniques, the properties of almost periodic function and the fluctuation lemma, this manuscript establishes the criteria for the existence and globally exponential stability of positive almost periodic solutions of a non-autonomous delayed Nicholson's blowflies model under weaker conditions, which refine and complement some existing literature. In particular, when the influence of delay disappears and the addressed model is autonomous, the adopted assumption in the obtained result is a sharp condition ensuring the global exponential stability of positive equilibrium points. Moreover, some numerical examples are provided to illustrate the effectiveness and feasibility of the theoretical findings. [ABSTRACT FROM AUTHOR]

We consider the discrete-time Arrow-Hurwicz-Uzawa primal-dual algorithm, also known as the first-order Lagrangian method, for constrained optimization problems involving a smooth strongly convex cost and smooth convex constraints. We prove that, for every given compact set of initial conditions, there always exists a sufficiently small stepsize guaranteeing exponential stability of the optimal primal-dual solution of the problem with a domain of attraction including the initialization set. Inspired by the analysis of nonlinear oscillators, the stability proof is based on a non-quadratic Lyapunov function including a nonlinear cross term. [ABSTRACT FROM AUTHOR]

This paper studies the fuzzy $ H_\infty $ H ∞ control of nonlinear DC microgrids subject to the dynamic event-triggered mechanism (ETM), aperiodic DoS attacks, noises and mismatching premises. First, using the information of DC microgrid's T-S fuzzy model and aperiodic DoS attacks, a discrete-time resilient dynamic ETM is proposed, which can save constrained system resources, as well as actively exclude attack-induced dropouts and Zeno behaviour. Second, a fuzzy switched system model is built, which provides a unified platform to evaluate effects of all the affecting factors such as the dynamic ETM and DoS attacks. Third, by constructing a piecewise Lyapunov functional, criteria for exponential stability with guaranteed $ H_\infty $ H ∞ performance are obtained, and an event-triggered fuzzy injection current controller is further designed. Simulation results confirm that, in the presence of aperiodic DoS attacks and noises, the proposed controller can stabilise the nonlinear DC microgrids, while the dynamic ETM works well in reducing the triggering rate without dropouts. Tradeoffs can be made between control and communication resources, and the proposed fuzzy controller achieves shorter settling times and smaller overshoots than the robust controller. [ABSTRACT FROM AUTHOR]

In this article, we develop stable and efficient numerical schemes for a binary fluid‐surfactant phase‐field model which consists of two Cahn–Hilliard type equations with respect to the free energy containing a Ginzburg–Landau double‐well potential, a logarithmic Flory–Huggins potential and a nonlinear coupling entropy. The numerical schemes, which are decoupled and linear, are established by the central difference spatial approximation in combination with the first‐ and second‐order exponential time differencing methods based on the convex splitting of the free energy. For the sake of the linearity of the schemes, the nonlinear terms, especially the logarithmic term, are approximated explicitly, which requires the bound preservation of the numerical solution to make the algorithm robust. We conduct the convergence analysis and prove the bound‐preserving property in details for both first‐ and second‐order schemes, where the high‐order consistency analysis is applied to the first‐order case. In addition, the energy stability is also obtained by the nature of the convex splitting. Numerical experiments are performed to verify the accuracy and stability of the schemes and simulate the dynamics of phase separation and surfactant adsorption. [ABSTRACT FROM AUTHOR]

Robust control of uncertain fully actuated systems (FASs) with nonlinear uncertainties and perturbed input matrices is considered. Motivated by the recent work on this issue, two novel robust controllers are further developed for two cases under different assumptions. For both cases, the assumption on the perturbation input matrix in the previous work is relaxed to a significant extent, which allows many typical perturbation input matrices, such as constant ones, to be handled, while the previous method cannot. Moreover, for the first case, the assumption on the system uncertainty is further relaxed, and the states of the closed-loop system are globally bounded and converge into an arbitrarily small spherical domain centered at the origin. For the second case, with another requirement on the system nonlinearity imposed, the global exponential stability of the closed-loop system is achieved. The successful application in an electromechanical system verifies the effectiveness of the method. • The nonlinear uncertainty and the uncertainty in the input matrix are considered. • A controller makes the states converge globally into an arbitrarily small region. • Another controller achieves the global exponential stability. • The assumptions on the perturbed input matrix in the previous work are relaxed. • A successful application in the control of electromechanical systems. [ABSTRACT FROM AUTHOR]

This paper introduces a fuzzy intermittent control issue for nonlinear PDE-ODE coupled system under spatially point measurements (SPMs), which can be represented by an ordinary differential equation (ODE) and a partial differential equation (PDE). Firstly, the nonlinear coupled system is aptly characterized by the Takagi–Sugeno (T–S) fuzzy PDE-ODE coupled model. Subsequently, based on T–S fuzzy model, a novel Lyapunov function (LF) is provided to design a fuzzy intermittent controller ensuring exponential stability of the closed-loop coupled system. The stabilization conditions are presented by means of a group of space-dependent linear matrix inequalities (SDLMIs). Finally, simulation results are given to illustrate the effectiveness of the proposed design method in the control of a hypersonic rocket car (HRC). [ABSTRACT FROM AUTHOR]

Keywords: Rational normal forms; Birkhoff normal forms; Nekhoroshev theorem; Gevrey norm; Hamiltonian PDEs.GraphBy Joackim Bernier; Nicolas Camps; Benoît Grébert and Zhiqiang WangReported by Author; Author; Author; Author [Extracted from the article]

This article focuses on the fault detection filtering problem for Itô stochastic Takagi–Sugeno (T‐S) fuzzy systems. In terms of line integral Lyapunov function, a sufficient condition of exponential stability in mean square and extended dissipativity for the systems under consideration is established which has less conservatism than the one based on quadratic Lyapunov function. The obtained sufficient condition is nonlinear, which makes the synthesis of fault detection filter being difficult and challenging. By choosing general matrix variables and constructing the appropriate orthogonal complement matrices, the nonlinear sufficient condition can be converted into linear one ingeniously via utilizing Finsler's lemma twice. Thus, the fault detection filter can be developed by virtue of parameterization. It should be pointed out that our filter determined by the parameterization approach includes the one obtained by the equivalent transformation method as a special case. Finally, we demonstrate the feasibility and superiority of our proposed approach through three numerical examples. [ABSTRACT FROM AUTHOR]

This paper investigates the exponential stability in mean square sense for a class of stochastic switched semi‐Markov jump systems (ssSMJS). In this model, a hierarchical control switched regulation is designed, considering the external stochastic disturbances and generally uncertain transition rates (TRs) of the entire system and making the system more general and practical. By using appropriate Lyapunov–Krasovskii functional, linear matrix inequality, Jensen inequality, and mode‐dependent average dwell time (MDADT), sufficient conditions on the exponential stability in mean square sense for ssSMJS are derived. Furthermore, a nonfragile state feedback controller is designed. Finally, two numerical examples are provided to demonstrate the effectiveness of the proposed criterion. [ABSTRACT FROM AUTHOR]

In this paper we study the stability of pullback exponential attractors with respect to perturbations for non-autonomous extensible coupled suspension bridge equations. The governing equations describe the vibration of the roadbed in the vertical plane and that of the main cable. Under quite general assumptions on nonlinear damping and sources terms and based on nonlinear semigroups and the theory of monotone operators, we establish existence and uniqueness of weak and strong solutions. By applying a criterion developed for continuous and non-autonomous models by Yang and Li [34], we construct a family of pullback exponential attractors stable with respect to perturbations. [ABSTRACT FROM AUTHOR]

AbstractIn this work, we focus on a one-dimensional initial-boundary value problem of a thermoelastic piezoelectric beam in the presence of magnetic effects with distributed delay acting in the mechanical equation. The well-posedness of the system is initially demonstrated by applying semigroup theory (Hille-Yosida theorem). Also, based on the construction of a Lyapunov functional, which is equivalent to the energy functional of the problem through multiplier techniques, we show that a unique dissipation through frictional damping is strong enough to ensure exponential stabilization of the model. Next, the results are compared to those of the electrostatic or quasi-static approaches. Moreover, we consider the fully dynamic and electrostatic or quasi-static piezoelectric beams with thermal effects, boundary feedback controllers and boundary distributed delays and using the multipliers technique, we establish an exponential stability result of the solution. Our results are related to the distributed delay weights. Finally, we give some numerical tests to illustrate the theoretical result. [ABSTRACT FROM AUTHOR]

This paper studies the problem of exponential stability of second moments of large-scale distribution-dependent stochastic differential equations (SDEs, in short). By introducing isolated subsystems, under certain hypotheses added on the interconnected terms and using the moment estimation, exponential stability of second moments of isolated subsystems implies exponential stability of second moments of large-scale distribution-dependent SDEs. Specially, we provide sufficient and necessary conditions for the exponential stability of large-scale distribution-dependent SDEs with triangular structure and apply this results to study stabilization of large-scale distribution-dependent SDEs. Finally, the main results are illustrated by several examples and applications. [ABSTRACT FROM AUTHOR]

This paper studies quasi‐sure exponential of triangular stochastic differential equations driven by G$$ G $$‐Brownian motion ( G$$ G $$‐SDEs, in short) with the help of the stability of each diagonal subsystems by exponential martingale inequality and G$$ G $$‐stochastic analysis techniques. This result allows us to study the full‐order filtering problem of the stochastic systems driven G$$ G $$‐Brownian motion. [ABSTRACT FROM AUTHOR]

This work focuses on a class of stochastic functional differential equations and neutral stochastic differential functional equations. By using a new approach, some sufficient conditions are obtained to guarantee the generalized mean square exponential stability for the equation under consideration. Certain existing results are refined and extended. Lastly, the validity of the main results is confirmed through several simulation examples. [ABSTRACT FROM AUTHOR]

This paper addresses the issue of event-triggered stabilization for neural networks vulnerable to replay attacks. According to the proposed event triggering mechanism and controller, the neural network is represented as a switched closed-loop system. Through the selection of a suitable Lyapunov function and applying Jensen's inequality, a criterion to ensure the mean square exponential stability of the system is established in the form of linear matrix inequalities. Building on this, a co-design method for the event trigger matrix and controller gain is given. Finally, a numerical example is used to verify the effectiveness of the method. [ABSTRACT FROM AUTHOR]

In this paper, we study the stochastic weak local exponential stability of stochastic differential systems with state‐dependent delay (SDD) subject to average‐delay impulses by using Lyapunov–Krasovskii functional and stochastic analytical skill. Unlike time‐dependent delay discussed in the previous literature, we introduce SDD in impulsive stochastic differential systems, where SDD is a stochastic variable associated with system state, consequently leading to an indeterminate delay boundary. Our findings reveal that when destabilizing delayed impulses satisfying specific conditions are generated, the stability of stochastic differential systems with destabilizing delayed impulses and stable continuous stochastic dynamics can still be maintained. Additionally, if stable delayed impulses satisfy certain conditions, stability of the systems under consideration can also be achieved, irrespective of the stable status on the continuous stochastic dynamics. Finally, two examples are given to demonstrate the validity of theoretical results. [ABSTRACT FROM AUTHOR]

This paper investigates anti-disturbance synchronization for Lur'e systems using a hierarchical composite control mechanism. This mechanism integrates two control approaches: disturbance observer-based control and switchedgain event-triggered control, ensuring the H∞ exponential stability of the synchronization-error system in the presence of multiple disturbances. A condition on the H∞ exponential stability is derived utilizing a piecewise-defined and timedependent Lyapunov function and several inequalities. Based on the condition, a co-design is proposed for the gains of the event-triggered controller and disturbance observer. For comparison, the hierarchical composite control with a fixed gain is also investigated, and the corresponding design approach is presented. Finally, the effectiveness of the proposed composite anti-disturbance synchronization control mechanism is validated through an example involving master-slave Chua's circuits. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the stabilization of the transmission problem of the degenerate wave equation and the heat equation under the Coleman–Gurtin heat conduction law or Gurtin–Pipkin law with the memory effect. We investigate the polynomial stability of this system when employing the Coleman–Gurtin heat conduction, establishing a decay rate of type t−4$t^{-4}$. Next, we demonstrate exponential stability in the case when Gurtin–Pipkin heat conduction is applied. [ABSTRACT FROM AUTHOR]

A version of the Floquet theory for first order delay differential equations is proposed. Formula of solutions representation is obtained. On this basis, the stability of first order delay differential equations is studied. An analogue of the classical integral Lyapunov–Zhukovskii test of stability is proved. New, in comparison with all known, tests of the exponential stability are obtained on the basis of the Floquet theory. A possibility to achieve the exponential stability is connected with oscillation of solutions. [ABSTRACT FROM AUTHOR]

We consider a C 0 -semigroup on a Banach space such that the resolvent is uniformly bounded on the right half-plane. In this paper we provide a condition on the resolvent which is sufficient and necessary for the uniform exponential stability of such a semigroup. As a consequence, we give an alternative proof of Gearhart's theorem (Trans. Amer. Math. Soc. 236, 385–394 (1978)). The approach lies on a complex inversion formula and tempered distributions. [ABSTRACT FROM AUTHOR]

In this work, a class of neutral-type Rayleigh equations involving $$D$$ D operators are proposed, where the damping item is a continuous $$T$$ T -anti-periodic function. Several new stability theorems are obtained to assure the $$T$$ T -anti-periodic exponential stability of the addressed equations by applying differential inequality analyses. Moreover, an illustrative example incorporating its graphical simulations is furnished to illustrate the validity of the derived findings. [ABSTRACT FROM AUTHOR]

In this paper, based on event-triggered control, the stabilisation problem of time-varying delay switched linear system with all subsystems unstable is studied. Firstly, the idea of event-triggered mechanism is introduced, and the state feedback controller is designed. Combining the discretised linear Lyapunov function method with the average dwell time technique, the stabilisation schemes for continuous switched system with unstable modes are obtained. Secondly, compared with existing results, the event-triggered mechanism scheme adopted under the current event-triggered control strategy reduces the number of system triggers, effectively saves computational resources, avoids Zeno's behaviour, and has better performance in terms of sampling frequency. Finally, the idea of event-triggered mechanism is first extended to discrete time-varying delay switched systems where all subsystems are unstable. By solving linear matrix inequalities, sufficient conditions for global exponential stability of the system are obtained. The effectiveness of this method was verified through a simulation example of a turbofan engine model. [ABSTRACT FROM AUTHOR]

In this paper, two novel classes of implicit exponential Runge–Kutta (ERK) methods are studied for solving highly oscillatory systems. First of all, symplectic conditions for two kinds of exponential integrators are derived, and we present a first-order symplectic method. High accurate implicit ERK methods (up to order four) are formulated by comparing the Taylor expansion of the exact solution, it is shown that the order conditions of two new kinds of exponential methods are identical to the order conditions of classical Runge–Kutta (RK) methods. Moreover, we investigate the linear stability properties of these exponential methods. Numerical examples not only present the long time energy preservation of the first-order symplectic method, but also illustrate the accuracy and efficiency of these formulated methods in comparison with standard ERK methods. [ABSTRACT FROM AUTHOR]

This paper aims to formulate a class of nonlinear hybrid stochastic time-delay neural networks (STDNNs) with Lévy noise. Specifically, the coefficients of networks grow polynomially instead of linearly, and the time delay of given neural networks is non-differentiable. In many practical situations, nonlinear hybrid STDNNs with Lévy noise are unstable. Hence, this paper uses feedback control based on discrete-time state and mode observations to stabilize the considered nonlinear hybrid STDNNs with Lévy noise. Then, we establish stabilization criteria of H ∞ stability, asymptotic stability, and exponential stability for the controlled nonlinear hybrid STDNNs with Lévy noise. Finally, a numerical example illustrating the usefulness of theoretical results is provided. [ABSTRACT FROM AUTHOR]

We establish an exponential stability result for a wave equation that includes weighted coefficients of structural damping and a delayed term. This study reveals cases where the delayed term may not be dominated by the damping term, yet the system is exponentially stable. Our coefficients do not obey necessarily the conditions that are usually imposed in the literature. [ABSTRACT FROM AUTHOR]

This article aimed to investigate the existence and stability of Besicovitch almost periodic ( B a p ) positive solutions for a stochastic generalized Mackey-Glass hematopoietic model. To begin with, we used stochastic analysis theory, inequality techniques, and fixed point theorems to prove the existence and uniqueness of L p -bounded and L p -uniformly continuous positive solutions for the model under consideration. Then, we used definitions to prove that this unique positive solution is also a B a p solution in finite-dimensional distributions. In addition, we established the global exponential stability of the B a p positive solution using reduction to absurdity. Finally, we provided a numerical example to verify the effectiveness of our conclusions. [ABSTRACT FROM AUTHOR]

In this study, we consider the initial boundary value problem of the planar magnetohydrodynamics (MHD) system when the viscous coefficients and heat conductivity depend on the temperature, which are assumed to be proportional to θα{\theta }^{\alpha }, α≥0\alpha \ge 0, and θβ{\theta }^{\beta }, β≥0\beta \ge 0, respectively, and magnetic diffusivity coefficient depends on the specific volume. We prove the existence and uniqueness of the global-in-time classical solution with general large initial data provided that α\alpha is sufficiently small and there is no restriction on the parameter β\beta . Moreover, the nonlinearly exponential stability of the solution is obtained. As a result, we extend the works given by Sun et al. for the full compressible Navier-Stokes equations and by Li and Shang for the full compressible MHD equations.