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1.
This paper investigates stability problems of a class of nonlinear impulsive switching systems with time-varying delays. Based on the common Lyapunov function method and Razumikhin technique, several stability criteria are established for nonlinear impulsive switching systems with time-varying delays. Our results show that switching systems can be stabilized by impulsive switching signals even if the system matrices are all unstable. In the absence of impulses, some of our results reduce to similar stability criteria for nonimpulsive switching systems in some recent research articles. Several examples with simulations are given to illustrate the efficiency of our results.  相似文献   

2.
In this paper, the robust exponential stability of uncertain impulsive delay difference equations is investigated. First, some robust exponential stability criteria for uncertain impulsive delay difference equations with continuous time in which the state variables on the impulses may relate to the time-varying delays are provided. Then a robust exponential stability result for uncertain linear impulsive delay difference equations with discrete time is given. Some examples, including an example which cannot be studied by the existing results, are also presented to illustrate the effectiveness of the obtained results.  相似文献   

3.
This paper investigates the problem of cluster synchronization of complex dynamical networks with noise and time-varying delays by using a delayed pinning impulsive control scheme. Different from the traditional impulsive control schemes without the effects of input delays, it designs a pinning impulsive control scheme to successfully address the aforementioned problem subject to impulsive input delays. By employing a time-dependent Lyapunov function and the mathematical induction, some novel criteria are established to guarantee the cluster synchronization of the noisy complex networks, revealing the closed relationship between the synchronization performance and the related factors, including the impulsive input delays, the number of the pinned nodes, the frequency and strength of the impulsive control, and the noisy perturbations. Some numerical examples and computer simulations are presented to illustrate the effectiveness of the theoretical results.  相似文献   

4.
This paper investigates the passivity and synchronization problems for two classes of multiple weighted coupled neural networks (MWCNNs) with or without time delays. Firstly, by utilizing an impulsive control strategy and some inequality techniques, several passivity criteria for MWCNNs with diverse dimensions of output and input are established. Then, based on the Lyapunov functional, some sufficient conditions to ensure the synchronization of MWCNNs via impulsive control are derived. In addition, combined with the comparison principle and the impulsive delay differential inequality, the global exponential synchronization of MWCNNs with time-varying delays is considered under impulsive control. Finally, two numerical examples illustrate the effectiveness of the obtained results.  相似文献   

5.
This paper investigates the pth moment exponential stability of impulsive stochastic functional differential equations. Some sufficient conditions are obtained to ensure the pth moment exponential stability of the equilibrium solution by the Razumikhin method and Lyapunov functions. Based on these results, we further discuss the pth moment exponential stability of generalized impulsive delay stochastic differential equations and stochastic Hopfield neural networks with multiple time-varying delays from the impulsive control point of view. The results derived in this paper improve and generalize some recent works reported in the literature. Moreover, we see that impulses do contribute to the stability of stochastic functional differential equations. Finally, two numerical examples are provided to demonstrate the efficiency of the results obtained.  相似文献   

6.
This paper investigates the problem of designing decentralized impulsive controllers for synchronization of a class of complex dynamical networks (CDNs) about some prescribed goal function. The CDNs are allowed to possess nonidentical nodes and coupling delays. Two cases of time-varying coupling delays are considered: the case where the coupling delays are uniformly bounded, and the case where the derivatives of the coupling delays are not greater than 1. The synchronization analysis for the first case is performed by applying a time-varying Lyapunov function based method combined with Razumikhin-type technique, while the synchronization analysis for the second case is conducted based on a time-varying Lyapunov functional based method. For each case, by utilizing a convex combination technique, the resulting synchronization criterion is formulated as the feasibility problem of a set of linear matrix inequalities (LMIs). Then, sufficient conditions on the existence of a decentralized impulsive controller are presented by employing these newly obtained synchronization criteria. The local impulse gain matrices can be designed by solving a set of LMIs. Finally, two representative examples are given to illustrate the correctness of the theoretical results.  相似文献   

7.
In this paper, the impulsive average-consensus problem of first-order multi-agent systems with dynamically changing topologies is investigated. Continuous-time dynamics and impulsive protocols are both subjected to effects from nonuniform time-varying communication delays. By utilizing Razumikhin techniques and time-varying Lyapunov function method, some impulse-delay-dependent sufficient criteria for the average-consensus of multi-agent systems are derived. In addition, the discrete-time connection digraph is designed in terms of linear matrix inequalities for given impulsive sequences and some programming skills are used to make the discrete-time topology meet the needs of the actual environment. Numerical simulations are given to illustrate the effectiveness and validity of the theoretical results.  相似文献   

8.
This paper is concerned with the problem of exponential synchronization of coupled complex networks with time-varying delays and stochastic perturbations (CCNTDSP). Different from previous works, both the internal time-varying delay and the coupling time-varying delay are taken into account in the network model. Meanwhile, an impulsive controller is designed to realize exponential synchronization in mean square of CCNTDSP. Combining the Lyapunov method with Kirchhoff’s Matrix Tree Theorem, some sufficient criteria are obtained to guarantee exponential synchronization in mean square of CCNTDSP. Furthermore, we apply the theoretical results to study exponential synchronization of stochastic coupled oscillators with the internal time-varying delay and the coupling time-varying delay. And a synchronization criterion is also obtained. Finally, two numerical examples are given to demonstrate the effectiveness and feasibility of our theoretical results and the superiority of impulsive control.  相似文献   

9.
This paper investigates the global asymptotic stability of stochastic fuzzy Markovian jumping neural networks with mixed delays under impulsive perturbations in mean square. The mixed delays include constant delay in the leakage term (i.e., “leakage delay”), time-varying delay and continuously distributed delay. By using the Lyapunov functional method, reciprocal convex approach, linear convex combination technique, Jensen integral inequality and the free-weight matrix method, several novel sufficient conditions are derived to ensure the global asymptotic stability of the equilibrium point of the considered networks in mean square. The proposed results, which do not require the differentiability and monotonicity of the activation functions, can be easily checked via Matlab software. Finally, two numerical examples are given to demonstrate the effectiveness and less conservativeness of our theoretical results over existing literature.  相似文献   

10.
《Journal of The Franklin Institute》2022,359(17):10017-10037
This paper investigates the positivity and stability of discrete-time coupled homogeneous systems with time-varying delays. First, an explicit criterion is given for the positivity of discrete-time coupled homogeneous delay systems. Then, by using the properties of homogeneous functions, a sufficient condition is presented for ensuring the stability of the considered systems. Moreover, the obtained result is applied to study the stability of positive singular systems with time-varying delay. It should be noted that it is the first time that the stability result is given for discrete-time coupled homogeneous positive systems with time-varying delays. Two numerical examples are presented to demonstrate the effectiveness of the derived results.  相似文献   

11.
This paper is concerned with the stability analysis of linear systems with time-varying delays. First, by introducing the quadratic terms of time-varying delays and some integral vectors, a more suitable Lyapunov-Krasovskii functional (LKF) is constructed. Second, two new delay-dependent estimation methods are developed in the stability analysis of linear system with time-varying delays, which include a reciprocally convex matrix inequality and an integral inequality. More information about time-varying delays and more free matrices are introduced into the two estimation approaches, which play a key role for obtaining an accurate upper bound of the integral terms in time derivative of LKFs. Third, based on the novel LKFs and new estimation approaches, some less conservative criteria are derived in the form of linear matrix inequality (LMI). Finally, three numerical examples are applied to verify the advantages and effectiveness of the newly proposed methods.  相似文献   

12.
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.  相似文献   

13.
This article concerns with stability analysis of discrete linear systems with time-varying delays. Firstly, we extend a quadratic function negative-determination lemma for a single variable to the bivariate case. Secondly, we construct a novel Lyapunov-Krasovskii functional (LKF) with a quadratically delay-dependent matrix to investigate the stability of discrete-time systems with time-varying delays. Based on the proposed lemma, a new delay-variation-dependent stability criterion is derived. Finally, numerical examples are given to illustrate the theoretical result and the proposed criterion is shown to be less conservative than some previous ones.  相似文献   

14.
In this paper, the global robust exponential stability problem for a class of uncertain inertial-type BAM neural networks with both time-varying delays is focused through Lagrange sense. The existence of time-varying delays in discrete and distributed terms is explored with the availability of lower and upper bounds of time-varying delays. Firstly, we transform the proposed inertial BAM neural networks to usual one. Secondly, by the aid of LKF, stability theory, integral inequality, some novel sufficient conditions for the global robust exponential stability of the addressed neural networks are obtained in terms of linear matrix inequalities, which can be easily tested in practice by utilizing LMI control toolbox in MATLAB software. Furthermore, many comparisons of proposed work are listed with some existing literatures to get less conservatism. Finally, two numerical examples are provided to demonstrate the advantages and superiority of our theoretical outcomes.  相似文献   

15.
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.  相似文献   

16.
This paper is devoted to investigating the robust stochastic exponential stability for reaction-diffusion Cohen–Grossberg neural networks (RDCGNNs) with Markovian jumping parameters and mixed delays. The parameter uncertainties are assumed to be norm bounded. The delays are assumed to be time-varying and belong to a given interval, which means that the lower and upper bounds of interval time-varying delays are available. Some criteria for delay-dependent robust exponential stability of RDCGNNs with Markovian jumping parameters are established in terms of linear matrix inequalities (LMIs), which can be easily checked by utilizing Matlab LMI toolbox. Numerical examples are provided to demonstrate the efficiency of the proposed results.  相似文献   

17.
In this paper, we investigate the consensus tracking problem of nonlinear MASs with nonuniform time-varying input delays and external disturbances. For each follower, the composited disturbance observer and the state observer are employed to estimate bounded composited disturbances and unmeasured states, and a distributed observer based on output-feedback is proposed to approximate the leader’s states approachably. Sequentially, the consensus tracking control is converted into a stability control problem for the nonlinear MASs with nonuniform time-varying input delays. Subsequently, a distributed controller based on the truncated prediction approach is presented, which only depends on the boundary value of time-varying input delays. The distributed controller can render each follower synchronically stable via the Lyapunov stability theory. Finally, a group of single-link manipulators is used as an example to verify the effectiveness of the theoretical results.  相似文献   

18.
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.  相似文献   

19.
In this paper, the problem of stability analysis for linear systems with time-varying delays is considered. By the consideration of new augmented Lyapunov functionals, improved delay-dependent stability criteria for asymptotic stability of the system are proposed for two cases of conditions on time-varying delays with the framework of linear matrix inequalities (LMIs), which can be solved easily by various efficient convex optimization algorithms. The enhancement of the feasible region of the proposed criteria is shown via three numerical examples by the comparison of maximum delay bounds.  相似文献   

20.
In this paper, an auxiliary model-based nonsingular M-matrix approach is used to establish the global exponential stability of the zero equilibrium, for a class of discrete-time high-order Cohen–Grossberg neural networks (HOCGNNs) with time-varying delays, connection weights and impulses. A new impulse-free discrete-time HOCGNN with time-varying delays and connection weights is firstly constructed, and the relationship between the solutions of original systems and new HOCGNNs is indicated by a technical lemma. From which, the global exponential stability criteria for the zero equilibrium are derived by using an inductive idea and the properties of nonsingular M-matrices. The effectiveness of the obtained stability criteria is illustrated by numerical examples. Compared with the previous results, this paper has three advantages: (i) The Lyapunov–Krasovskii functional is not required; (ii) The obtained global exponential stability criteria are applied to check whether a matrix is a nonsingular M-matrix, which can be conveniently tested; (iii) The proposed approach applies to most of discrete-time system models with impulses and delays.  相似文献   

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