Further analysis on global robust exponential stability of neural networks with time-varying delays

In this paper, an approach based on H-matrix theory and Halanay inequality is developed to present a sufficient condition for global robust exponential stability of interval neural networks with time-varying delays. Theoretic analysis shows that our result includes a previous result derived in the literature. Finally, some numerical examples are given to show the effectiveness of the obtained results.     

Global exponential stability of impulsive discrete-time neural networks with time-varying delays

This paper studies the problem of global exponential stability and exponential convergence rate for a class of impulsive discrete-time neural networks with time-varying delays. Firstly, by means of the Lyapunov stability theory, some inequality analysis techniques and a discrete-time Halanay-type inequality technique, sufficient conditions for ensuring global exponential stability of discrete-time neural networks are derived, and the estimated exponential convergence rate is provided as well. The obtained results are then applied to derive global exponential stability criteria and exponential convergence rate of impulsive discrete-time neural networks with time-varying delays. Finally, numerical examples are provided to illustrate the effectiveness and usefulness of the obtained criteria.     

Stability analysis of impulsive parabolic complex networks

In the present paper, two kinds of impulsive parabolic complex networks (IPCNs) are considered. In the first one, all nodes have the same time-varying delay. In the second one, different nodes have different time-varying delays. Using the Lyapunov functional method combined with the inequality techniques, some global exponential stability criteria are derived for the IPCNs. Furthermore, several robust global exponential stability conditions are proposed to take uncertainties in the parameters of the IPCNs into account. Finally, numerical simulations are presented to illustrate the effectiveness of the results obtained here.     

Global robust exponential stability analysis for stochastic interval neural networks with time-varying delays

In this paper, the global exponential stability is investigated for a class of stochastic interval neural networks with time-varying delays. The parameter uncertainties are assumed to be bounded in given compact sets. Based on Lyapunov stable theory and stochastic analysis approaches, the delay-dependent criteria are derived to ensure the global, robust, exponential stability of the addressed system in the mean square. The criteria can be checked easily by the LMI control toolbox in Matlab. A numerical example is given to illustrate the effectiveness and improvement over some existing results.     

Exponential stability results for uncertain neutral systems with interval time-varying delays and Markovian jumping parameters

This paper deals with the global exponential stability analysis of neutral systems with Markovian jumping parameters and interval time-varying delays. The time-varying delay is assumed to belong to an interval, which means that the lower and upper bounds of interval time-varying delays are available. A new global exponential stability condition is derived in terms of linear matrix inequality (LMI) by constructing new Lyapunov-Krasovskii functionals via generalized eigenvalue problems (GEVPs). The stability criteria are formulated in the form of LMIs, which can be easily checked in practice by Matlab LMI control toolbox. Two numerical examples are given to demonstrate the effectiveness and less conservativeness of the proposed methods.     

Global robust stability of interval cellular neural networks with time-varying delays

This paper studies the global robust asymptotic stability (GRAS) and global robust exponential stability (GRES) of delayed cellular neural networks with time-varying delays. A series of new criteria concerning GRAS and GRES are obtained by employing the Young's inequality, Halanay's inequality and Lyapunov functional and combine with some analysis techniques. Several previous results are improved and generalized. Some examples and remarks are also given to illustrate the effectiveness of the results. In addition, these criteria possess important leading significance in design and applications of global stable DCNNs, and are of great interest in many applications.     

Novel global robust exponential stability criterion for uncertain BAM neural networks with time-varying delays

In this paper, the global robust exponential stability for a class of delayed BAM neural networks with norm-bounded uncertainty is studied. Some less conservative conditions are presented for the global exponential stability of BAM neural networks with time-varying delays by constructing a new class of Lyapunov functionals combined with free-weighting matrices. This novel approach, based on the linear matrix inequality (LMI) technique, removes some existing restrictions on the system’s parameters, and the derived conditions are easy to verify via the LMI toolbox. Comparisons between our results and previous results admit that our results establish a new set of stability criteria for delayed BAM neural networks.     

非自治变时滞Cohen-Grossberg网络的Lagrange稳定性和全局指数吸引集

基于考虑两种不同类型的激活函数,本文研究了非自治变时滞Cohen-Grossberg神经网络（CGNN）在Lagrange意义下的全局指数稳定性,通过利用新的不等式技巧和构造恰当的Lyapunov泛函给出非自治变时滞CGNN模型在Lagrange意义下全局指数稳定性（即一致有界性）以及对其全局指数吸引集估计的代数判据,并给出应用例子加以验证.     

Some improved criteria for global robust exponential stability of neural networks with time-varying delays

In this paper, some sufficient conditions for global robust exponential stability of interval neural networks with time-varying delays are presented. It is shown that our results include some counterparts of the previous literatures. On basis of the obtained results, some linear matrix inequality (LMI) criteria are derived. Moreover, three numerical examples and a simulation are given to show the effectiveness of the obtained results.     

Exponential stability and applications of switched positive linear impulsive systems with time-varying delays and all unstable subsystems

The global uniform exponential stability of switched positive linear impulsive systems with time-varying delays and all unstable subsystems is studied in this paper, which includes two types of distributed time-varying delays and discrete time-varying delays. Switching behaviors dominating the switched systems can be either stabilizing and destabilizing in the new designed switching sequence. We design new linear programming algorithm process to find the feasible ratio of stabilizing switching behaviors, which can be compensated by unstable subsystems, destabilizing switching behaviors, and impulses. Specically, we add a kind of nonnegative impulses which is consistent with the switching behaviors for the systems. Employing a multiple co-positive Lyapunov-Krasovskii functional, we present several new sufficient stability criteria and design new switching sequence. Then, we apply the obtained stability criteria to the exponential consensus of linear delayed multi-agent systems, and obtain the new exponential consensus criteria. Three simulations are provided to demonstrate the proposed stability criteria.     

Robust exponential stability and stabilizability of linear parameter dependent systems with delays

The robust exponential stability and stabilizability problems are addressed in this paper for a class of linear parameter dependent systems with interval time-varying and constant delays. In this paper, restrictions on the derivative of the time-varying delay is not required which allows the time-delay to be a fast time-varying function. Based on the Lyapunov-Krasovskii theory, we derive delay-dependent exponential stability and stabilizability conditions in terms of linear matrix inequalities (LMIs) which can be solved by various available algorithms. Numerical examples are given to illustrate the effectiveness of our theoretical results.     

变时滞Hopfield神经网络的全局吸引性和全局指数稳定性

对一类具时滞的Hopfeild型神经网络模型,在非线性神经元激励函数只要求满足Lipschitz连续的条件下,利用推广的Halanay时延微分析不等式、Dini导数以及泛函微分析技术,给出了这类模型的平衡点全局指数稳定性和全局吸引性的充分条件,这些条件易于检验,且改进和推广了前人的结论.此外,此文给出了研究神经网络模型的全局吸引性的微分不等式比较方法.     

Robust Exponential Stability of Stochastically Nonlinear Jump Systems with Mixed Time Delays

In this paper, the problem of robust exponential stability is investigated for a class of stochastically nonlinear jump systems with mixed time delays. By applying the Lyapunov–Krasovskii functional and stochastic analysis theory as well as matrix inequality technique, some novel sufficient conditions are derived to ensure the exponential stability of the trivial solution in the mean square. Time delays proposed in this paper comprise both time-varying and distributed delays. Moreover, the derivatives of time-varying delays are not necessarily less than 1. The results obtained in this paper extend and improve those given in the literature. Finally, two numerical examples and their simulations are provided to show the effectiveness of the obtained results.     

Delay-dependent exponential stability of cellular neural networks with time-varying delays

The global exponential stability of cellular neural networks (CNNs) with time-varying delays is analyzed. Two new sufficient conditions ensuring global exponential stability for delayed CNNs are obtained. The conditions presented here are related to the size of delay. The stability results improve the earlier publications. Two examples are given to demonstrate the effectiveness of the obtained results.     

Neural networks with discrete and distributed time-varying delays: A general stability analysis

In this paper, the global asymptotic and exponential stability are investigated for a class of neural networks with both the discrete and distributed time-varying delays. By using appropriate Lyapunov–Krasovskii functional and linear matrix inequality (LMI) technique, several delay-dependent sufficient conditions are obtained to guarantee the global asymptotic and exponential stability of the addressed neural networks. These conditions are expressed in terms of LMIs, and are dependent on both the discrete and distributed time delays. Therefore, the stability of the neural networks can be checked readily by resorting to the Matlab LMI toolbox. In addition, the proposed stability criteria do not require the monotonicity of the activation functions and the differentiability of the discrete and distributed time-varying delays, which means that our results generalize and further improve those in the earlier publications. A simulation example is given to show the effectiveness and less conservatism of the obtained conditions.     

WEIGHTED PSEUDO ALMOST-PERIODIC SOLUTIONS OF SHUNTING INHIBITORY CELLULAR NEURAL NETWORKS WITH MIXED DELAYS

In this paper,we prove the existence and the global exponential stability of the unique weighted pseudo almost-periodic solution of shunting inhibitory cellular neural networks with mixed time-varying delays comprising different discrete and distributed time delays.Some sufficient conditions are given for the existence and the global exponential stability of the weighted pseudo almost-periodic solution by employing fixed point theorem and differential inequality techniques.The results of this paper complement the previously known ones.Finally,an illustrative example is given to demonstrate the effectiveness of our results.     

Analysis of global exponential stability and periodic solutions of FCNNs with constant delays and time-varying delays

In this paper, we investigate a class of fuzzy cellular neural networks with constant delays and time-varying delays. By constructing suitable Lyapunov functional and employing Young inequality, we find sufficient conditions for the existence, uniqueness, global exponential stability of equilibrium, and the existence of periodic solutions of fuzzy cellular neural networks with time-varying delays. The results of this paper are new and they extend previously known results.     

A graph-theoretic approach to exponential stability of BAM neural networks with delays and reaction-diffusion

This paper deals with the problem of global exponential stability for bidirectional associate memory (BAM) neural networks with time-varying delays and reaction-diffusion terms. By using some inequality techniques, graph theory as well as Lyapunov stability theory, a systematic method of constructing a global Lyapunov function for BAM neural networks with time-varying delays and reaction-diffusion terms is provided. Furthermore, two different kinds of sufficient principles are derived to guarantee the exponential stability of BAM neural networks. Finally, a numerical example is carried out to demonstrate the effectiveness and applicability of the theoretical results.     

Global exponential stability for a class of retarded functional differential equations with applications in neural networks

In this paper, the global exponential stability and asymptotic stability of retarded functional differential equations with multiple time-varying delays are studied by employing several Lyapunov functionals. A number of sufficient conditions for these types of stability are presented. Our results show that these conditions are milder and more general than previously known criteria, and can be applied to neural networks with a broad range of activation functions assuming neither differentiability nor strict monotonicity. Furthermore, the results obtained for neural networks with time-varying delays do not assume symmetry of the connection matrix.     

Some criteria for robust stability of Cohen–Grossberg neural networks with delays

This paper considers the problem of robust stability of Cohen–Grossberg neural networks with time-varying delays. Based on the Lyapunov stability theory and linear matrix inequality (LMI) technique, some sufficient conditions are derived to ensure the global robust convergence of the equilibrium point. The proposed LMI conditions can be checked easily by recently developed algorithms solving LMIs. Comparisons between our results and previous results admits our results establish a new set of stability criteria for delayed Cohen–Grossberg neural networks. Numerical examples are given to illustrate the effectiveness of our results.