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This paper investigates the problems of exponential stability for a class of quaternion‐valued memristor‐based neural networks. By using M‐matrix theory and fixed point theorem, the existence and uniqueness of the equilibrium point of quaternion‐valued neural network are proved, respectively. Then, by combining M‐matrix with exponential stability theory, a non‐factorization method is obtained by using some inequality techniques to give the effective conditions of global exponential stability of quaternion‐valued memristor‐based neural network with time‐varying delay. Finally, numerical examples are given to demonstrate the validity of the derived results. [ABSTRACT FROM AUTHOR]

This article is concerned with the issue of observer‐based event‐triggered H∞$$ {H}_{\infty } $$ control for networked switched systems (NSSs) under hybrid attacks. Since hybrid attacks can cause more damage to the system than a single cyber attack, this article considers a situation where stochastic deception attacks and aperiodic denial‐of‐service (DoS) attacks coexist in NSSs. To address this issue, the dynamics of the initial switched system combined with the event‐triggered mechanism (ETM), observers and hybrid attacks are formulated as a new augmented switched system. Thereinto, the unmeasurable states are estimated by a newly constructed gain adjustable observer and an observer state‐based adaptive ETM is designed under DoS attacks to save limited communication resources. Then, employing the Lyapunov stability theory and average dwell time (ADT) approach, sufficient conditions are obtained to guarantee the mean‐square exponential stability with a H∞$$ {H}_{\infty } $$ performance index of the new model. And the quantitative relationship between the switching signal and DoS attacks is formulated. Moreover, a co‐design method of ETM parameters and observer‐based controller gains is proposed. Compared with some existent results, restrictions on DoS attack signals and switching signals are relaxed. Finally, a numerical example is utilized to verify the feasibility and effectiveness of the proposed theory. [ABSTRACT FROM AUTHOR]

This paper is devoted to dealing with the issue of the estimation of the domain of attraction (DOA) for highly nonlinear neutral complex networks (HNNCNs) with time delays. Firstly, by the Razumikhin approach, we establish several novel lemmas on the estimation of DOA for highly nonlinear neutral differential systems. The cases of bounded non-differentiable delays and unbounded proportional delays are discussed, respectively. Subsequently, by utilizing the proposed lemmas, combining the Lyapunov stability theory and inequality technique, the estimation of DOA on HNNCNs with bounded delays or proportional delays is derived when the chosen control gain is sufficiently large. If initial values start from DOA, then the states of systems will exponentially or polynomially converge to the equilibrium point, which means that the local exponential or polynomial synchronization of HNNCNs is realized. Additionally, the weighted outer-coupling matrix of complex networks is not required to be symmetric, which means that the derived results can be applied to both the undirected networks and directed networks. Finally, several numerical examples are provided to illustrate the feasibility of theoretical findings. [ABSTRACT FROM AUTHOR]

This article is concerned with the practical stability performance of nonlinear impulsive stochastic functional differential systems driven by G-Brownian motion (G-ISFDSs). Comparing with traditional Lyapunov stability theory, practical stability can portray qualitative behaviour and quantitative properties of suggested systems. By employing G-Itô formula, Lyapunov–Razumikhin approach and stochastic analysis theory, some novel conditions for pth moment practical exponential stability and quasi-sure global practical uniform exponential stability of G-ISFDSs are established. The obtained results show that impulses may influence dynamic behaviour of the addressed system. Two numerical examples are given to verify the validity of our developed results. [ABSTRACT FROM AUTHOR]

Practical stability can describe qualitative behavior and quantitative properties of systems in comparison with traditional Lyapunov stability theory. In this paper, such stability problem is formulated for nonlinear delayed urban traffic systems described by uncertain differential equations which are a type of differential equations driven by Liu processes. First of all, we prove the existence and uniqueness of the solution. Then, we analyze the pth moment practically exponential stability and quasi surely globally practically uniformly exponential stability of the system by employing general It'o formula, Gronwall's inequality, Holder inequality and Borel-Cantelli lemma. Moreover, an example is presented to verify the validity of our theoretical methods. [ABSTRACT FROM AUTHOR]

This paper investigates the stability in an exponential sense of complex-valued Bidirectional Associative Memory (BAM) neural networks with time delays under the stochastic and impulsive effects. By utilizing the contracting mapping theorem, the existence and uniqueness of the equilibrium point for the proposed complex-valued neural networks are verified. Moreover, based on the Lyapunov - Krasovskii functional construction, matrix inequality techniques and stability theory, some novel time-delayed sufficient conditions are attained in linear matrix inequalities (LMIs) form, which ensure the exponential stability of the trivial solution for the addressed neural networks. Finally, to illustrate the superiority and effects of our theoretical results, two numerical examples with their simulations are provided via MATLAB LMI control toolbox. [ABSTRACT FROM AUTHOR]

The present study introduces a new adaptive control framework that aims to attain exponential stability in complex‐valued neural network systems utilizing memristors while accounting for time‐varying delays. The control issues in systems of this nature are mostly attributed to the presence of memristors and time‐varying latency. To overcome these challenges and achieve stabilization outcomes, a methodology is employed that integrates adaptive control approaches inside a matrix‐based framework. This study employs Lyapunov's stability theory to establish exponential stabilization conditions and conduct convergence analysis. The efficacy of the suggested control algorithm in achieving exponential stabilization and robustness under varied delays is demonstrated through numerical simulations. [ABSTRACT FROM AUTHOR]

This paper primarily focuses on the chaos synchronisation analysis of neural networks (NNs) under a hybrid controller. Firstly, we design a suitable hybrid controller with saturated impulse control, combined with time-dependent intermittent control. Both controls are low-energy consumption and discrete, aligning well with industrial development needs. Secondly, the saturation function in the chaotic neural network is addressed using the polyhedral representation method and the sector nonlinearity method, respectively. By integrating the Lyapunov stability theory, Jensen's inequality, the mathematical induction method, and the inequality reduction technique, we establish suitable time-dependent Lyapunov generalised equations. This leads to the estimation of the domain of attraction and the derivation of local exponential stability conditions for the error system. The validity of the achieved theoretical criteria is eventually demonstrated through numerical experiment simulations. [ABSTRACT FROM AUTHOR]

The synchronization control problem of discrete-time switched neural networks is considered in this paper. Wherein, the switchings among subsystems are described by the mode-dependent persistent dwell-time switching rule. Due to restricted network bandwidth resources, a dynamic event-triggered mechanism is introduced to alleviate the frequency of data transmission. In addition, the activation function dividing method is utilized to make the result less conservative. Then, using Lyapunov stability theory, several sufficient criteria are obtained to ensure that the synchronization error system can achieve mean-square exponential stability and meet the specified passive performance under DoS attacks. Based on these criteria, the concrete form of controller gain is solved. Finally, numerical examples demonstrate the rationality and superiority of the proposed method. [ABSTRACT FROM AUTHOR]

In this article, the Input-to-state stability theory is used to investigate the stochastic Cohen–Grossberg bidirectional associative memory neural network with time-varying delay. In addition, Markovian jump parameters are considered in this model to determine the continuous-time, discrete-state Markov chain. By utilizing Lyapunov functional and weak infinitesimal generator the algebraic conditions are derived for Input-to-state criteria. In the end, a numerical example is given to show the merits of the given method. [ABSTRACT FROM AUTHOR]

Exponential stability criteria for neutral second-order stochastic systems involving impulses and state-dependent delay have been addressed in this paper based on stability theory, stochastic analysis, and the inequality technique. Some sufficient conditions are given to establish the exponential stability of such systems, which is well-established in the deterministic case, but less known for the stochastic case. In our model, the noise effect can be described as a symmetric Wiener process. By formulating the impulsive integral technique, exponential stability analysis of the pth moment of the second-order system involving stochastic perturbation is established. As an application that illustrates the theoretical formulation, an example is presented. [ABSTRACT FROM AUTHOR]

This article focuses on investigating a dynamic output feedback control issue for uncertain nonlinear networked control systems (NCSs) in the presence of Denial-of-Service (DoS) attacks and sensor failures. By using the low and upper membership functions (LUMFs) of interval type-2 (IT2) Takagi-Sugeno (T-S) fuzzy model, the uncertainties existing in the considered NCSs are depicted effectively. Based on the IT2 fuzzy system, a switching fuzzy model is further established to correspond to different DoS attack scenarios. According to the average dwell-time approach and Lyapunov stability theory, an IT2 fuzzy dynamic output feedback control scheme is proposed so that the exponential stability of the considered NCSs can be achieved regardless of DoS attacks and sensor failures. Lastly, illustrative examples are presented to confirm the theoretical results proposed in this paper. [ABSTRACT FROM AUTHOR]

We investigate the synchronizability of multilayer star-ring networks. Two types of multilayer networks, including aggregated coupling and divergent coupling, are established based on the connections between the hub node and the leaf nodes in the subnetwork. The eigenvalue spectrum of the two types of multilayer networks is strictly derived, and the correlation between topological parameters and synchronizability is analyzed by the master stability function framework. Moreover, the variable coupling strength has been investigated, revealing that it is significantly related to the synchronizability of the aggregated coupling while having no influence on the divergent coupling. Furthermore, the validity of the synchronizability analysis is obtained by implementing adaptive control on the multilayer star-ring networks previously mentioned. Calculations and comparisons show that the differences caused by the sizes of multilayer networks and interlayer coupling strength are not negligible. Finally, numerical examples are also provided to validate the effectiveness of the theoretical analysis. [ABSTRACT FROM AUTHOR]

This article investigates the problems of the exponential stability and the decentralized control for a class of interconnected delayed systems subject to nonlinear disturbance and control input saturation. Firstly, a model of the interconnected system with time delays, nonlinear disturbance and input saturation is established. Secondly, based on stability theory, Newton–Leibnitz formula and relevant inequality technique, some useful lemmas are derived, and stability analysis of the interconnected system is presented. Meanwhile, a decentralized controller with two control laws is designed. The obtained stability results can also be used for physical systems such as multi‐area interconnected power systems and chaotic systems. At last, the effectiveness of the stability results and the proposed control method is demonstrated by a few examples. [ABSTRACT FROM AUTHOR]

Ayala-Gilpin ecosystem is one of the most famous differential equation models based on experimental and theoretical analysis. Most of the previous works on the almost periodic solution and its stability are mainly about the existence of an almost-periodic solution and its global stability. In fact, the real ecosystem presents multiple stable states due to the influence of various external factors. However, there are few researches on multiple almost-periodic solutions and local stability of Ayala-Gilpin ecosystem. Therefore, we focus on the existence and local exponential stability of multiple almost-periodic solutions for a classical nonlinear competitive Ayala-Gilpin ecosystem provided with varying-lags and control terms in this paper. Firstly, a class of functions having only two zeros in (− ∞ , + ∞) is investigated. Next, based on the existence of zeros of these functions, we obtain some sufficient conditions to ensure the existence of at least four almost-periodic positive solutions by utilising theorem of coincidence degree and some inequality techniques. Furthermore, we also conclude that this ecosystem exists at least two almost-periodic positive solutions under relatively weak conditions. Finally, we build some Lyapunov functionals to discuss the local exponential stability of each almost-periodic positive solution in its own region. As an application, a numerical simulation inspect the effectiveness of our major results. [ABSTRACT FROM AUTHOR]

This paper investigates the exponential stability of a class of neutral inertial neural networks with multi-proportional delays and leakage delays. By utilizing the Lyapunov stability theory, the approach of parametric variation, and the differential inequality technique, some criteria are acquired that can guarantee that all solutions of the addressed system converge exponentially to the equilibrium point. In particular, the neutral term, multi-proportional delays, and leakage delays are incorporated simultaneously, resulting in a more general model, and the findings are novel and refine the previous works. Finally, one example is provided to indicate that the dynamic behavior is consistent with the theoretical analysis. [ABSTRACT FROM AUTHOR]

In this paper, the stability of a linear Timoshenko beam system involved with infinite memory is considered. Different from the previous results on where the monotony of kernel is always fulfilled, the memory kernel under consideration is assumed to be non-monotonic. The well-posedness of the system is obtained by means of resolvent family theory and the exponential stability is proved under certain conditions. Numerical simulations are also presented to verify the main results. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a new type of stability for nonlinear impulsive systems of differential equations, namely practical h-stability. By using the Lyapunov stability theory, some sufficient conditions which guarantee practical h-stability are established. Our original results generalize well-known fundamental stability results, practical stability, practical exponential stability and practical asymptotic stability for nonlinear time-varying impulsive systems. Then two classes of nonlinear impulsive systems, namely perturbed and cascaded impulsive systems, are discussed. Furthermore, the problem of practical h-stabilization for certain classes of nonlinear impulsive systems is considered. Finally, two numerical examples are given to show the effectiveness of our theoretical results. [ABSTRACT FROM AUTHOR]

This paper addresses the problem of stabilization of non-minimum phase switched nonlinear systems where the internal dynamics with symmetries or non-symmetries of each mode may be unstable. The authors initially build a stabilizing Lyapunov controller for each mode in order to stabilize its own unstable internal dynamics. The proposed approach is based on the exact input-output feedback linearization technique and the Lyapunov stability theory. The stability results for non-minimum phase switched nonlinear systems with arbitrary switching rules are then obtained using generalized Gronwall–Bellman inequalities. Finally, numerical examples are provided to demonstrate the efficacy of the achieved results. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the problem of stability with respect to a part of variables of nonlinear time-varying systems. We derive some sufficient conditions that guarantee exponential stability and practical exponential stability with respect to a part of the variables of perturbed systems based on Lyapunov techniques where converse theorems are stated. Furthermore, illustrative examples to show the usefulness and applicability of the theory of stability with respect to a part of variables are provided. In particular, we show that our approach can be applied to the spring-mass-damper model. [ABSTRACT FROM AUTHOR]

In this work we study a Nicholson-type periodic system with variable delay, density-dependent mortality and linear harvesting rate. Using the topological degree and Lyapunov stability theories, we obtain sufficient conditions that allow us to demonstrate the existence of periodic solutions for the Nicholson-type system and, under suitable conditions, the uniqueness and local exponential stability of the periodic solution is established. We illustrate our results with an example and numerical simulations. [ABSTRACT FROM AUTHOR]

The aim of this paper is to give some discrete and continuous versions of Barbashin type theorems for the uniform polynomial stability and instability of evolution families in Banach spaces, by using Banach sequence spaces in ℋ ⁢ (ℕ ≥ 1) and Banach function spaces in ℋ ⁢ (ℝ ≥ 1) , respectively. Variants for uniform polynomial stability and instability of some well-known results in the exponential stability theory and polynomial stability theory are obtained. [ABSTRACT FROM AUTHOR]

This article reports on exponential synchronization for stochastic coupled neural networks (NNs) with mixed time‐varying delays, stochastic coupling strength, and Markovian switching. In order to reduce the amount of data transmission and save network resources, an event‐triggered control method is provided in this study. When the triggered condition can be met, the data can be transmitted so that the master and slave systems with limited resources and bandwidth can realize synchronization. By the Lyapunov stability theory and several analysis skills of matrix properties, some new criteria are obtained to make sure that stochastic coupled NNs are mean square exponential stability. These criteria are provided by linear matrix inequalities. Finally, a numerical case further demonstrates the validity of the proposed criteria. [ABSTRACT FROM AUTHOR]

In this paper, a class of quaternion-valued BAM neural networks (QVBAMNNs) fractional-order model with impulses and proportional delays is proposed in discrete-time case. The QVBAMNNs fractional-order model is investigated directly rather than through real decomposition method or the plural one. By employing homeomorphic mapping theorem, Lyapunov stability theory and inequality technology, several criteria for the discrete-time QVBAMNNs fractional-order model are derived to guarantee the existence, uniqueness and global exponential stability (GES) of equilibrium point. The novelty of these results comes from the generality with the fractional-order systems and the integer-order ones. Finally, two examples are given to demonstrate the effectiveness and availability of the derived criteria. [ABSTRACT FROM AUTHOR]

This article presents a novel dynamic event-triggered scheme for the load frequency regulation with periodic denial-of-service (DoS) attacks and deception attacks via decentralized output-based control algorithm. Compared with the existing event-triggered strategy, the proposed one automatically changes the parameters of the triggered condition by detecting the frequency trend of the DoS attack to change the release frequency, which can ensure the stability of the power system while increasing the probability of effective transmission subject to DoS attack and thus, reducing network bandwidth usage. First, the proposed dynamic event-triggered strategy combined with the decentralized output-based controller is presented in a unified framework to deal with deception attacks and DoS attacks in the multiarea power system. Then, we utilize the Lyapunov stability theory to analyze the exponential stability in the mean-square sense and the robustness of the power system. By solving a set of linear matrix inequalities (LMIs), a procedure is given for the design of output-based load frequency controllers. Finally, a three-area power system is exploited as a simulation to verify the effectiveness of the proposed results. [ABSTRACT FROM AUTHOR]

Successive lag synchronization (SLS) is a novel and important synchronization pattern, whose control problem has been deeply investigated in the past several years. However, the impact of noise perturbation on the control of SLS is still unclear. To this end, this paper focuses on the intermittent pinning control of SLS on a dynamical network with noise perturbation. In order to push the SLS to a desired trajectory, we design an intermittent pinning control scheme that is active only on controlled intervals and a small proportion of nodes. By applying the stability theory of stochastic differential equation, we obtain sufficient conditions under which the network can realize the SLS with exponential stability in mean square. According to these conditions, we can determine which nodes should be controlled or not, the minimum control ratio and the impact of noise perturbation on the SLS. An interesting finding is that performing the control on at least half of each subinterval can ensure the stochastic stability of SLS, which is independent of any network parameters. The effectiveness of proposed intermittent pinning control scheme is verified by the network of coupled Chua's circuits. [ABSTRACT FROM AUTHOR]

Benefit from the significant work of Song and Mao (2018), this paper focuses on the almost sure exponential stability of hybrid stochastic delayed Cohen–Grossberg neural network (SDCGNN) with the nonlinear disturbance. By virtue of stationary distribution, Lyapunov stability theory and LMI tool, we will propose that if the corresponding delay‐free stochastic neural network is almost surely exponentially stable, then there exists a positive number τ∗ such that the SDCGNN is also almost surely exponentially stable so long as τ < τ∗. Finally, an example is given to verify the effectiveness of our results, and an implicit lower bound for τ∗ is provided. [ABSTRACT FROM AUTHOR]

This paper studies the attitude tracking control of a flexible airship subjected to wind disturbances, actuator saturation and control surface faults. Efficient flexible airship models, including elastic deformation, rigid body motions, and their coupling, are established via Lagrange theory. A fast-nonsingular terminal sliding-mode (NTSM) combined with a backstepping control is proposed for the problem. The benefits of this approach are NTSM merits of high robustness, fast transient response, and finite time convergence, as well as the backstepping control in terms of globally asymptotic stability. However, the major limitation of the backstepping NTSM is that its design procedure is dependent on the prior knowledge of the bound values of the disturbance and faults. To overcome this limitation, a wind observer is designed to compensate for the effect of the wind disturbances, an anti-windup compensator is designed to compensate for actuator saturation, and an adaptive fault estimator is designed to estimate the faults of the control surfaces. Globally exponential stability of the closed-loop control system is guaranteed by using the Lyapunov stability theory. Finally, simulation results demonstrate effectiveness and advantages of the proposed control for the Skyship-500 flexible airship, even in the presence of unknown wind disturbances, control surface faults, and different stiffness variants. [ABSTRACT FROM AUTHOR]

In this paper, we mainly study the almost sure exponential stability of impulsive stochastic differential delay equations (ISDDEs) with bounded variable delays. The main technique is to compare ISDDEs with corresponding impulsive stochastic differential equations (ISDEs) without delay, to obtain the upper bound τ ∗ of delays that ISDDEs can maintain stability by accurate calculation. The results show that if the corresponding ISDEs are almost surely exponentially stable, then the ISDDEs are also almost surely exponentially stable as long as these delays are less than τ ∗. In addition, the stability theory established in this paper can be applied to noise stabilization based on sampled-data observations of a class of unstable impulsive systems. Taking impulsive Lurie systems (ILSs) as an example, we discuss the design of noise stabilization strategies. • The almost sure exponential stability of impulsive stochastic delay differential equations is established. • The positive impact of noise and impulse jump on impulsive stochastic delay differential equations is discussed. • A noise stabilization strategy for impulse systems based on sampled-data observations is proposed. [ABSTRACT FROM AUTHOR]

In chemical, biological, or population (epidemiological) processes the feedback action may be considerably delayed by time-consuming chemical measurements or biological tests. With such large delays on the control action in mind, and motivated by the fact that in some of these systems only piecewise-constant inputs can be applied between time instants at which measurements trigger changes in control, we consider the problem of event-triggered stabilization of 1-D reaction–diffusion PDE systems with input delay. The approach relies on reformulating the delay problem as an actuated transport PDE which cascades into the reaction–diffusion PDE, and on the emulation of backstepping control. The paper proposes a static (state-dependent) triggering condition which establishes the time instants at which the control value needs to be updated. It is shown that under the proposed event-triggered boundary control, there exists a minimal dwell-time (independent of the initial conditions) between two triggering times which allows to guarantee the well-posedness of the closed-loop system, and the exponential stability. The stability analysis is based on Input-to-State stability theory for PDEs and small-gain arguments. A simulation example is presented to validate the theoretical results. [ABSTRACT FROM AUTHOR]

This note is concerned with the observer‐based distributed control problem of large‐scale systems under gossip communication protocol. Random binary variables that satisfy a certain conditional probability distribution are introduced to model gossip communication protocol. In such a protocol, each subcontroller receives information from only one randomly chosen neighbor at each instant. Novel observer‐based distributed controllers are proposed for large‐scale systems. Based on Lyapunov stability theory and stochastic matrix manipulations, sufficient conditions are established such that the closed‐loop system is exponentially mean square stable and the prescribed L2‐gain performance is satisfied. Then these conditions are transformed into linear matrix inequalities. The observer gains and controller gains can be obtained by solving a set of linear matrix inequalities. Finally, two numerical examples are used to illustrate the effectiveness of the proposed theoretical results. [ABSTRACT FROM AUTHOR]

In this article, the observer-based $\mathcal {L}_{2}-\mathcal {L}_{\infty }/ \mathcal {H}_{\infty }$ mixed control issue for uncertain nonlinear plants in the presence of measurement outliers is investigated under interval type-2 (IT2) Takagi–Sugeno (T–S) fuzzy approach. Through using lower and upper membership functions, the uncertainties that exist in nonlinear systems can be captured efficaciously. For the sake of reducing the effect of abrupt abnormal signals that disturb the measurements utilized for the purpose of state estimation, a novel fuzzy observer is designed via utilizing the adaptive saturation of output errors. After that, sufficient conditions are derived to ensure the exponential stability with a mixed $\mathcal {L}_{2}- \mathcal {L}_{\infty }/\mathcal {H}_{\infty }$ performance level of considered systems on the basis of Lyapunov stability theory. Finally, the usefulness of the new designed control approach is confirmed through two demonstrative simulation examples. [ABSTRACT FROM AUTHOR]

This article addresses the distributed secure platoon control of connected vehicles with denial-of-service (DoS) attack phenomena, which may occur at some sampling time instant. First, a switched time-delay system model is introduced, which captures the time-varying sampling and the DoS attack phenomena simultaneously. Then, sufficient conditions are obtained based on the Lyapunov stability theory, the Jensen’s Inequality method, and the topology matrix decoupling technique, such that the vehicle platoon system under consideration achieves an exponential tracking performance. In this article, the presented system design conditions establish several quantitative relationships between attack parameters and system performance. Moreover, the critical values of attack frequency (AF) and the sampling interval (SI) are also derived, respectively. Finally, both of the simulation and experiment studies on a network of four vehicles are introduced to validate the design. [ABSTRACT FROM AUTHOR]

Copyright of Baghdad Science Journal is the property of Republic of Iraq Ministry of Higher Education & Scientific Research (MOHESR) and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

This paper addresses the stabilization problem of a microscale beam system subject to a delay. Several situations are considered depending whether the delay occurs as a boundary or interior/distributed term. In both cases, the microbeam system is shown to be well posed in the sense of semigroups theory of linear operators. More importantly, using the energy method, the exponential stability is established as long as the parameter of the delay term is small. [ABSTRACT FROM AUTHOR]

Copyright of Journal of Jilin University (Science Edition) / Jilin Daxue Xuebao (Lixue Ban) is the property of Zhongguo Xue shu qi Kan (Guang Pan Ban) Dian zi Za zhi She and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

This paper investigates the global exponential synchronization problem of switching genetic oscillator networks with time-varying delays by using a newly-designed partial impulsive control scheme. This scheme is only required to control partial molecules of each gene node, different from the traditional pinning impulsive control scheme, in which all the molecules of the chosen nodes are assumed to be under control. Besides, both the number of controlled molecules and the impulsive strength of the presented control scheme are mode-dependent, either identical or different with respect to different topologies. Based on the Lyapunov stability theory and comparison principle, the sufficient criteria for guaranteeing the exponential synchronization of genetic oscillator networks with finite arbitrarily switching topologies are established. Finally, two illustrative examples are presented to verify the main results. [ABSTRACT FROM AUTHOR]

This paper considers the Clifford-valued recurrent neural network (RNN) models, as an augmentation of real-valued, complex-valued, and quaternion-valued neural network models, and investigates their global exponential stability in the Lagrange sense. In order to address the issue of non-commutative multiplication with respect to Clifford numbers, we divide the original n-dimensional Clifford-valued RNN model into 2 m n real-valued models. On the basis of Lyapunov stability theory and some analytical techniques, several sufficient conditions are obtained for the considered Clifford-valued RNN models to achieve global exponential stability according to the Lagrange sense. Two examples are presented to illustrate the applicability of the main results, along with a discussion on the implications. [ABSTRACT FROM AUTHOR]

Connected vehicles (CVs) have demonstrated significant potential for addressing traffic issues. This paper presents a mathematical framework for stochastic heterogeneous traffic flow, integrating regular vehicles (RVs) and CVs, considering stochasticity, driver's dynamic time headway (DTH) characteristics, and the information flow topology (IFT) of CVs. We develop a novel car-following model (CFM) for RVs, accounting for both driver's stochasticity and DTH characteristics. Furthermore, we propose a dynamic model for CVs by integrating connected assisted driving strategies (CADS) into the RVs' model, which includes a dynamic information flow topology (DIFT) based on the time headway (TH) between vehicles within the communication range. We derive second-order exponential stability conditions for both RVs and CVs by employing the Lyapunov stochastic stability theory. We investigate the impact of driver stochasticity, DTH characteristics, and CADS on heterogeneous traffic flow characteristics through extensive numerical experiments. Model calibration results indicate that, in comparison to the state-of-the-art model, the proposed model exhibits superior prediction accuracy, achieving a 9.09% improvement at the group-driver level and a 10.47% improvement at the individual-driver level. Theoretical and numerical experimental results demonstrate that CVs with the proposed assisted driving strategy effectively mitigate traffic oscillations, and traffic flow stability improves as the CV penetration rate increases. Moreover, CVs can efficiently suppress stochasticity in traffic flow, with the strength of traffic fluctuations decreasing as the CV penetration rate grows. Different CV spatial distributions result in different propagation strengths of disturbances in traffic flow, adhering to a specific dual Gaussian distribution. Under various conditions, the average decline rates of speed fluctuations and energy consumption for traffic with the increasing CV penetration rate are 20%–50% and 10%–30%, respectively. • Proposed a novel CFM for RVs considering driver's DTH and stochasticity. • Developed a dynamic model for CVs by integrating CADS into the RVs' model. • Derived second-order exponential stability conditions for both RVs and CVs. • The impacts of driver stochasticity, DTH and CADS on traffic flow characteristics are studied. [ABSTRACT FROM AUTHOR]

This paper proposes a barrier function-based adaptive control strategy with a nonlinear sliding surface for a class of uncertain dynamic systems with input saturation. Its main objectives are to ensure robustness to parametric and non-parametric uncertainties whilst eliminating the reaching phase. A global nonlinear switching surface is defined and an adaptive barrier function sliding mode control approach is derived. The barrier strategy is adopted to ensure the convergence of the states to the desired values without overestimating the control gains. System stability is analyzed using the Lyapunov stability theory. The control parameters are obtained using the linear matrix inequality (LMI) approach. The control law is designed to remove the reaching phase. The effectiveness of the proposed approach was validated using a simulation study. The proposed control approach can easily be implemented to various nonlinear uncertain systems. [ABSTRACT FROM AUTHOR]

The exponential synchronization of non-autonomous chaotic systems with uncertain parameters was studied. The adaptive controller was designed. Based on the Lyapunov stability theory, the exponential stability of the error system was proved. Furthermore, the synchronization time was controlled through adjustment of the control parameters. Numerical simulations of 2 non-autonomous chaotic systems with uncertain parameters were presented to illustrate the ability and effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

The importance of prediction for genetic regulatory network (GRNs) makes mathematical modeling a prominent tool. In this paper, we consider weighted pseudo-almost periodic solutions for a class of GRNs with time-varying delays. We establish the existence, uniqueness, and global exponential stability by employing the theory of dichotomy, the fixed point theorem, and differential inequality. A numerical example along with a graphical illustration are presented to support our main results. Our results extend existing GRNs models using almost periodic functions to support a wider range of regulatory processes. [ABSTRACT FROM AUTHOR]

In this paper, the exponential stability in mean square for Markovian jumping systems (MJSs) is discussed. A new dynamic model, which involves parameters uncertainties, nonlinearities, and Lévy noises, is proposed. Moreover, an adaptive sliding mode controller is built to study the stability of such a complex model. First, an integral-type sliding mode surface (SMS) is established to obtain the sliding mode motion dynamics of MJSs. By the generalized Itô formula and the Lyapunov stability theory, some sufficient conditions are obtained to make sure the exponential stability in mean square for the sliding mode motion dynamics. Second, an adaptive sliding mode control law is provided to assure the reachability of the specified SMS. Furthermore, corresponding parameters of the sliding mode controller and the SMS can be got by solving the convex optimization problem. Finally, the validity of the stability results obtained is illustrated by a numerical simulation and a practical simulation. [ABSTRACT FROM AUTHOR]