ROBUST GLOBAL EXPONENTIAL STABILITY OF UNCERTAIN IMPULSIVE SYSTEMS

By using the quasi-Lyapunov function, some sufficient conditions of global exponential stability for impulsive systems are established, which is the basis for the following discussion. Then, by employing Riccati inequality and Hamilton-Jacobi inequality approach, some sufficient conditions of robust exponential stability for uncertain linear/nonlinear impulsive systems are derived, respectively. Finally, some examples are given to illustrate the applications of the theory.

Global exponential stability of Cohen-Grossberg neural networks with variable delays

A class of generalized Cohen-Grossberg neural networks（CGNNs） with variable de- lays are investigated. By introducing a new type of Lyapunov functional and applying the homeomorphism theory and inequality technique, some new conditions axe derived ensuring the existence and uniqueness of the equilibrium point and its global exponential stability for CGNNs. These results obtained are independent of delays, develop the existent outcome in the earlier literature and are very easily checked in practice.

GLOBAL ATTRACTIVITY AND GLOBAL EXPONENTIAL STABILITY FOR DELAYED HOPFIELD NEURAL NETWORK MODELS

Some global properties such as global attractivity and global exponential stability for delayed Hopfield neural networks model, under the weaker assumptions on nonlinear activation functions, are concerned. By constructing suitable Liapunov function, some simpler criteria for global attractivity and global exponential stability for Hopfield continuous neural network,; with time delays are presented.

Global exponential stability of mixed discrete and distributively delayed cellular neural network

This paper concernes analysis for the global exponential stability of a class of recurrent neural networks with mixed discrete and distributed delays. It first proves the existence and uniqueness of the balance point, then by employing the Lyapunov-Krasovskii functional and Young inequality, it gives the sufficient condition of global exponential stability of cellular neural network with mixed discrete and distributed delays, in addition, the example is provided to illustrate the applicability of the result.

New results on global exponential stability of competitive neural networks with different time scales and time-varying delays

This paper studies the global exponential stability of competitive neural networks with different time scales and time-varying delays. By using the method of the proper Lyapunov functions and inequality technique, some sufficient conditions are presented for global exponential stability of delay competitive neural networks with different time scales. These conditions obtained have important leading significance in the designs and applications of global exponential stability for competitive neural networks. Finally, an example with its simulation is provided to demonstrate the usefulness of the proposed criteria.

Global exponential stability for delayed cellular neural networks and estimate of exponential convergence rate

Some sufficient conditions for the global exponential stability and lower bounds on the rate of exponential convergence of the cellular neural networks with delay (DCNNs) are obtained by means of a method based on delay differential inequality. The method, which does not make use of any Lyapunov functional, is simple and valid for the stability analysis of neural networks with delay. Some previously established results in this paper are shown to be special casses of the presented result.

Global exponential stability of switched systems

This paper proposes a method for the stability analysis of deterministic switched systems.Two motivational examples are introduced （nonholonomic system and constrained pendulum）.The finite collection of models consists of nonlinear models,and a switching sequence is arbitrary.It is supposed that there is no jump in the state at switching instants,and there is no Zeno behavior,i.e.,there is a finite number of switches on every bounded interval.For the analysis of deterministic switched systems,the multiple Lyapunov functions are used,and the global exponential stability is proved.The exponentially stable equilibrium of systems is relevant for practice because such systems are robust to perturbations.

Global Exponential Stability of Almost Periodic Solution of Cellular Neural Networks with Time-Varying Delays

In this paper, global exponential stability of almost periodic solution of cellular neural networks with time-varing delays （CNNVDs） is considered. By using the methods of the topological degree theory and generalized Halanay inequality, a few new applicable criteria are established for the existence and global exponential stability of almost periodic solution. Some previous results are improved and extended in this letter and one example is given to illustrate the effectiveness of the new results.

Global exponential stability of cellular neural networks with time delays

By using the properties of nonnegative matrices and techniques of differential inequalities,some sufficient conditions for the global exponential stability of cellular neural networks with time delays were obtained.The criteria do not require such conditions as boundedness and differentiability of activation functions.The conditions of the theorem were verified.

Novel criteria for global exponential stability and periodic solutions of delayed Hopfield neural networks

The global exponentially stability and the existence of periodic solutions of a class of Hopfield neural networks with time delays are investigated. By constructing a novel Lyapunov function, new criteria are provided to guarantee the global exponentially stability of such systems. For the delayed Hopfield neural networks with time-varying external inputs, new criteria are also acquired for the existence and exponentially stability of periodic solutions. The results are generalizations and improvements of some recent achievements reported in the literature on networks with time delays.

GLOBAL EXPONENTIAL STABILITY IN HOPFIELD AND BIDIRECTIONAL ASSOCIATIVE MEMORY NEURAL NETWORKS WITH TIME DELAYS

Without assuming the boundedness, strict monotonicity and differentiability of the activation functions, the authors utilize the Lyapunov functional method to analyze the global convergence of some delayed models. For the Hopfield neural network with time delays, a new sufficient condition ensuring the existence, uniqueness and global exponential stability of the equilibrium point is derived. This criterion concerning the signs of entries in the connection matrix imposes constraints on the feedback matrix independently of the delay parameters. From a new viewpoint, the bidirectional associative memory neural network with time delays is investigated and a new global exponential stability result is given.

Existence and Global Exponential Stability of Pseudo Almost Periodic Solutions of a General Delayed BAM Neural Networks

This paper studies a class of general BAM neural networks with multiple delays. Em- ploying the exponential dichotomy theory and fixed point method, together with constructing suitable Lyapunov functionals, easily verifiable delay-independent criteria are established to ensure the exis- tence and global exponential stability of pseudo almost periodic solutions, which not only generalize but also complement some existing ones. These theoretical results are also supported with numerical simulations.

GLOBAL EXPONENTIAL STABILITY TO A CLASS OF DIFFERENTIAL SYSTEM WITH DELAY

The global exponential stability of the zero solution to a class of differential system with delay is considered. By constructing a suitable type of Lyapunov functional and using some analytical techniques, we derive some criteria to check exponential stability of this system. The results establish a relation between the delay time and the parameters of the system. Two examples are also given to illustrate the validity of the results.

Existence and Global Exponential Stability of Periodic Solutions for General Shunting Inhibitory Cellular Neural Networks with Delays

By using the Leray-Schauder fixed point theorem,differential inequality techniques and constructing suitable Lyapunov functional,several sufficient conditions are obtained for the existence and global exponential stability of periodic solutions for general shunting inhibitory cellular neural networks with delays.Some new results are obtained and some previously known results are improved.An example is employed to illustrate our feasible results.

Global exponential stability of cellular neural networks with multi-proportional delays

In this paper, a class of cellular neural networks （CNNs） with multi-proportional delays is studied. The nonlinear transformation yi（t） = xi（et） transforms a class of CNNs with multi-proportional delays into a class of CNNs with multi-constant delays and time- varying coefficients. By applying Brouwer fixed point theorem and constructing the delay differential inequality, several delay-independent and delay-dependent sufficient conditions are derived for ensuring the existence, uniqueness and global exponential stability of equilibrium of the system and the exponentially convergent rate is estimated. And several examples and their simulations are given to illustrate the effectiveness of obtained results.

Global Exponential Stability of Fuzzy Cellular Neural Networks with Impulses and Infinite Delays

In this paper, the global exponential stability of fuzzy cellular neural networks with impulses and infinite delays is investigated. Based on an impulsive delayed integro-differential inequality and the properties of fuzzy logic operation and M-matrix, an easily verified sufficient condition is obtained. Moreover, the exponential convergent rate for the fuzzy cellular neural networks with impulses and infinite delays is also given. An example is given to illustrate the effectiveness of our theoretical result.

A new result on global exponential robust stability of neural networks with time-varying delays

In this paper, the global exponential robust stability of neural networks with ume-varying delays is investigated. By using nonnegative matrix theory and the Halanay inequality, a new sufficient condition for global exponential robust stability is presented. It is shown that the obtained result is different from or improves some existing ones reported in the literatures. Finally, some numerical examples and a simulation are given to show the effectiveness of the obtained result.

Global Exponential Stability of a Class of Neural Networks with Delays

This paper is concerned with the stability of neural networks with time-varying delays. Under assumption that the nonlinear stimulate functions are Lipschitz continuous, by means of generalized Halanay inequalities, Dini＇s derivative and functional analysis techniques, several globally exponential stability criteria are established, which are only dependent on the parameters of the system.

Exponential stability and existence of periodic solutions for a class of recurrent neural networks with delays

Both the global exponential stability and the existence of periodic solutions for a class of recurrent neural networks with continuously distributed delays （RNNs） are studied. By employing the inequality α∏k=1^m bk^qk≤1/r ∑qkbk^r＋1/rα^r（α≥0,bk≥0,qk〉0,with ∑k=1^m qk=r-1,r≥1, constructing suitable Lyapunov r k=l k=l functions and applying the homeomorphism theory, a family of simple and new sufficient conditions are given ensuring the global exponential stability and the existence of periodic solutions of RNNs. The results extend and improve the results of earlier publications.

Exponential stability for uncertain neutral systems with Markov jumps

This paper deals with the global exponential stability problems for stochastic neutral Markov jump systems （MJSs） with uncertain parameters and multiple time-delays. The delays are respectively considered as constant and time varying cases, and the uncertainties are assumed to be norm bounded. By selecting appropriate Lyapunov-Krasovskii functions, it gives the sufficient condition such that the uncertain neutral MJSs are globally exponentially stochastically stable for all admissible uncertainties. The stability criteria are formulated in the form of linear matrix inequalities （LMIs）, which can be easily checked in practice. Finally, two numerical examples are exploited to illustrate the effectiveness of the developed techniques.