Exponential stability of switched linear impulsive time-varying system and its application

This paper aims at the problem of exponential stability for switched linear impulsive time-varying system. By constructing two different switched discretized Lyapunov functions, some new sufficient conditions ensuring the global exponential stability of switched linear impulsive time-varying system are provided, which can be employed to the case when all subsystems are unstable. Furthermore, we apply theoretical results to the consensus of multi-agent system with switching topologies. Finally, numerical examples demonstrate the effectiveness of given results.     

An optimization approach to static output-feedback control of LTI positive systems with delayed measurements

In this paper, we investigate the static output-feedback stabilization problem for LTI positive systems with a time-varying delay in the state and output vectors. By exploiting the induced monotonicity, necessary and sufficient conditions ensuring exponential stability of the closed-loop system are first quoted. Based on the derived stability conditions, necessary and sufficient stabilization conditions are formulated in terms of matrix inequalities. This general setting is then transformed into suitable vertex optimization problems by which necessary and sufficient conditions for the existence of a desired static output-feedback controller are obtained. The proposed synthesis conditions are presented in the form of linear programming conditions, which can be effectively solved by various convex algorithms.     

Global exponential robust stability of Cohen-Grossberg neural network with time-varying delays and reaction-diffusion terms

In this paper, the global exponential robust stability is investigated for Cohen-Grossberg neural network with time-varying delays and reaction-diffusion terms, this neural network contains time-invariant uncertain parameters whose values are unknown but bounded in given compact sets. Neither the boundedness and differentiability on the activation functions nor the differentiability on the time-varying delays are assumed. By using general Halanay inequality and M-matrix theory, several new sufficient conditions are obtained to ensure the existence, uniqueness, and global exponential robust stability of equilibrium point for Cohen-Grossberg neural network with time-varying delays and reaction-diffusion terms. Several previous results are improved and generalized, and three examples are given to show the effectiveness of the obtained results.     

Stability analysis problems of periodic piecewise polynomial systems

This paper studies the stability analysis problems of periodic piecewise systems, in which subsystems are given in the time-varying polynomial forms. A Lyapunov function with continuous time-varying Lyapunov matrix is adopted, which relaxes constraints on the variation of Lyapunov function in each subsystem. Using the time interval information, the exponential stability and stabilizing controller synthesis are studied. The results provide a possible alternative method to study the general periodic time-varying systems, which may further support the analysis and synthesis of general periodic systems. The effectiveness of the proposed method is validated and illustrated via numerical examples.     

Global exponential stability for multi-group neutral delayed systems based on Razumikhin method and graph theory

This paper is concerned with the global exponential stability for an original class called coupled systems of multi-group neutral delayed differential equations (MNDDEs). By employing Razumikhin method along with graph theory, sufficient conditions are established to guarantee the global exponential stability of MNDDEs, which are in the form of Razumikhin theorem. For the convenience of use, sufficient conditions in the form of coefficients are also obtained. Furthermore, coefficient-type criterion is employed to study the stability of coupled neutral delay oscillators which shows the applicability of our findings. Finally, two numerical examples are given to demonstrate the validity and feasibility of the theoretical results.     

Existence and exponential stability of almost periodic solution for neutral delay BAM neural networks with time-varying delays in leakage terms

This paper is concerned with a class of neutral delay BAM neural networks with time-varying delays in leakage terms. Some sufficient conditions are established to ensure the existence and exponential stability for such class of neural networks by employing the exponential dichotomy of linear differential equations, fixed point theorems and differential inequality techniques. An example is provided to show the effectiveness of the theoretical results. The results of this paper are completely new and complementary to the previously known results.     

Existence and global exponential stability of a periodic solution for a discrete-time interval general BAM neural networks

In this paper, a discrete-time interval general BAM bidirectional associative memory neural networks model is considered. By employing the theory of coincidence degree and using Halanay-type inequality technique we establish new sufficient conditions ensuring the existence and global exponential stability of periodic solutions for the discrete-time interval general BAM bidirectional neural networks. The results obtained generalize and improve known results in [23]. An example is provided to show the correctness of our analysis.     

Parameter-dependent robust stability for uncertain Markovian jump systems with time delay

In this paper, the problem of parameter-dependent robust stability analysis is addressed for uncertain Markovian jump linear systems (MJLSs) with polytopic parameter uncertainties and time-varying delay. By constructing parameter-dependent Lyapunov functional, some sufficient conditions are developed to enable robust exponential mean square stability for the systems. New parameter-dependent robust stability criteria for MJLSs are established in the form of linear matrix inequalities (LMIs), which can be solved efficiently by the interior-point algorithm. Finally, a numerical example is given to demonstrate the effectiveness of the proposed approach.     

Exponential stability of time-controlled switching systems with time delay

This paper studies the exponential stability of the nonlinear time-controlled switching systems with delay. Two Lyapunov-type stability theorems for such systems with and without state jumps at switching instants are developed, and the corresponding exponential convergence rates are estimated. Numerical examples are given to show the validity of theoretical results.     

Discrete Razumikhin-type stability theorems for stochastic discrete-time delay systems

By using the Razumikhin-type technique, for stochastic discrete-time delay systems, this paper establishes the discrete Razumikhin-type theorems on the pth moment stability, the global pth moment stability and the pth moment exponential stability, respectively. The almost sure exponential stability is also investigated by using the pth moment exponential stability and the Borel–Cantelli lemma. As the applications of t he established theorems, stability of a special class of stochastic discrete-time delay systems, synchronization of the stochastic discrete-time delay dynamical networks and stabilization of a stochastic discrete-time linear delay time invariant system are examined.     

Exponential stability and boundedness of nonlinear perturbed systems by unbounded perturbation terms

We study the exponential stability and boundedness problem for perturbed nonlinear time-varying systems using Lyapunov Functions with indefinite derivatives. As the limiting function for the perturbation term, we use different forms and give stability and boundedness conditions in terms of the coefficients in these bounds. Contrary to most of the available conditions, we allow the coefficients to be unbounded. But instead, we put forward a condition that requires a series produced by coefficients to be limited and exponentially decaying. We perform our results on Linear time-varying systems and generalize many of the available results.     

Stability robustness of linear output feedback systems with both time-varying structured and unstructured parameter uncertainties as well as delayed perturbations

This paper investigates the stability robustness of linear output feedback systems with both time-varying structured (elemental) and unstructured (norm-bounded) parameter uncertainties as well as delayed perturbations by directly considering the mixed quadratically coupled uncertainties in the problem formulation. Based on the Lyapunov approach and some essential properties of matrix measures, two new sufficient conditions are proposed for ensuring that the linear output feedback systems with delayed perturbations as well as both time-varying structured and unstructured parameter uncertainties are asymptotically stable. The corresponding stable region, that is obtained by using the proposed sufficient conditions, in the parameter space is not necessarily symmetric with respect to the origin of the parameter space. Two numerical examples are given to illustrate the application of the presented sufficient conditions, and for the case of only considering both the delayed perturbations and time-varying structured parameter uncertainties, it can be shown that the results proposed in this paper are better than the existing one reported in the literature.     

Exponential stability and stabilization of a class of uncertain linear time-delay systems

This paper presents new exponential stability and stabilization conditions for a class of uncertain linear time-delay systems. The unknown norm-bounded uncertainties and the delays are time-varying. Based on an improved Lyapunov-Krasovskii functional combined with Leibniz-Newton formula, the robust stability conditions are derived in terms of linear matrix inequalities (LMIs), which allows to compute simultaneously the two bounds that characterize the exponential stability rate of the solution. The result can be extended to uncertain systems with time-varying multiple delays. The effectiveness of the two stability bounds and the reduced conservatism of the conditions are shown by numerical examples.     

Exponential synchronization of fractional-order reaction-diffusion coupled neural networks with hybrid delay-dependent impulses

This paper is concentrated on exploring the exponential synchronization of reaction-diffusion coupled neural networks with fractional-order and impulses. Firstly, an extended Halanay-type inequality is established to cope with the hybrid delay-dependent impulsive problem by utilizing the mathematical induction. Furthermore, a direct error method is introduced by constructing Lyapunov function for the addressed networks to investigate the exponential synchronization under impulsive effects. By utilizing the technique of average impulsive interval and strength, some sufficient synchronization criteria are derived, which are closely associated with time delay and the commensurate order for fractional-order systems. Lastly, three numerical examples are presented to demonstrate the correctness for established results.     

Stability analysis for switched genetic regulatory networks: An average dwell time approach

In this correspondence, the problem of exponential stability for switched genetic regulatory networks (GRNs) with time delays is investigated. The GRNs are composed of N modes and the network switches from one mode to another. By employing the piecewise Lyapunov functional method combined with the average dwell time approach and by using a novel Lyapunov–Krasovskii functional (LKF), sufficient criteria are given to ensure the exponential stability for the switched GRNs with constant and time-varying delays, respectively. These criteria are proved to be much less conservative than the most recent results, since the results reported in this paper not only depend on the delay bounds, but also depend on the partitioning. All the conditions presented here are in the form of matrix inequalities which are easy to be verified via the Matlab toolbox. Two examples are provided in the end of this paper to illustrate the effectiveness of the obtained theoretical results.     

Dissipative output feedback control for semi-Markovian jump systems under hybrid cyber-attacks

In this paper, the dissipativity-based dynamic output feedback controller (DOFC) design for Semi-Markovian jump systems under stochastic cyber-attacks is first proposed. It is assumed that the time-varying uncertainties obey Bernoulli-distribution and transition probability matrix is time-varying and partially accessed. By utilizing the dissipativity-based technique, sufficient conditions for the existence of the DOFC are obtained to ensure the exponential stability with a strict dissipative performance of the resulted system. Next, the proposed results are improved by fractionalizing the time-varying transition probability matrix and the corresponding DOFC gains are obtained by cone complementarity linearization algorithm. Simulations results are provided to demonstrate the effectiveness and theoretical value of the proposed dissipativity-based DOFC design method.     

New delay dependent robust asymptotic stability for uncertain stochastic recurrent neural networks with multiple time varying delays

This paper is concerned with the stability analysis problem for a class of delayed stochastic recurrent neural networks with both discrete and distributed time-varying delays. By constructing a suitable Lyapunov–Krasovskii functional, a linear matrix inequality (LMI) approach is developed to establish sufficient conditions to ensure the global, robust asymptotic stability for the addressed system in the mean square. The conditions obtained here are expressed in terms of LMIs whose feasibility can be checked easily by MATLAB LMI Control toolbox. In addition, two numerical examples with comparative results are given to justify the obtained stability results.     

Dynamics of linear delayed systems with decaying disturbances

Dynamical systems in the real world are always subject to various disturbances. This paper studies the dynamics of linear delayed systems with decaying disturbances, both discrete- and continuous-time cases are considered. It is first shown that if an unforced linear system is exponentially stable, then the disturbed system has a dynamical property like exponential stability provided that the disturbance decays at an exponential rate, and has a dynamical property like asymptotic stability provided that the disturbance asymptotically approaches zero. These results are then applied to block triangular systems in the presence of time-varying delays, leading to criteria for checking the stability properties of this class of systems by considering diagonal blocks of system matrices. Particularly, a block triangular system is exponentially stable if and only if each system described by the diagonal blocks of system matrices is exponentially stable. Finally, a numerical example is presented to illustrate the theoretical results.     

Finite-time stability and stabilization of linear discrete time-varying stochastic systems

This paper studies the finite-time stability and stabilization of linear discrete time-varying stochastic systems with multiplicative noise. Firstly, necessary and sufficient conditions for the finite-time stability are presented via a state transition matrix approach. Secondly, this paper also develops the Lyapunov function method to study the finite-time stability and stabilization of discrete time-varying stochastic systems based on matrix inequalities and linear matrix inequalities (LMIs) so as to Matlab LMI Toolbox can be used.The state transition matrix-based approach to study the finite-time stability of linear discrete time-varying stochastic systems is novel, and its advantage is that the state transition matrix can make full use of the system parameter informations, which can lead to less conservative results. We also use the Lyapunov function method to discuss the finite-time stability and stabilization, which is convenient to be used in practical computations. Finally, three numerical examples are given to illustrate the effectiveness of the proposed results.     

Switching signal design for exponential stability of discrete switched systems with interval time-varying delay

The switching signal design for global exponential stability of discrete switched systems with interval time-varying delay is considered in this paper. Some LMI conditions are proposed to design the switching signal and guarantee the global exponential stability of switched time-delay system. Some nonnegative inequalities are used to reduce the conservativeness of the systems. Finally, two numerical examples are illustrated to show the main result.