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.

Generalized LMI-based approach to global asymptotic stability of cellular neural networks with delay

A global asymptotic stability problem of cellular neural networks with delay is investigated. A new stability condition is presented based on the Lyapunov-Krasovskii method, which is dependent on the amount of delay. A result is given in the form of a linear matrix inequality, and the admitted upper bound of the delay can be easily obtained. The time delay dependent and independent results can be obtained, which include some previously published results. A numerical example is given to show the effectiveness of the main results.

Almost sure exponential stability of neutral stochastic delayed cellular neural networks

In this paper, almost sure exponential stability of neutral delayed cellular neural networks which are in the noised environment is studied by decomposing the state space to sub-regions in view of the saturation linearity of output functions of neurons of the cellular neural networks. Some algebraic criteria are obtained and easily verified. Some examples are given to illustrate the correctness of the results obtained.

Exponential Stability for Delayed Cellular Neural Networks

The exponential stability of the delayed cellular neural networks （DCNN＇s） is investigated. By dividing the network state variables into some parts according to the characters of the neural networks, some new sufficient conditions of exponential stability are derived via constructing a Liapunov function. It is shown that the conditions differ from previous ones. The new conditions, which are associated with some initial value, are represented by some blocks of the interconnection matrix.

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 analysis of cellular neural networks with multiple time delays

Global exponential stability problems are investigated for cellular neural networks （CNN） with multiple time-varying delays. Several new criteria in linear matrix inequality form or in algebraic form are presented to ascertain the uniqueness and global exponential stability of the equilibrium point for CNN with multiple time-varying delays and with constant time delays. The proposed method has the advantage of considering the difference of neuronal excitatory and inhibitory effects, which is also computationally efficient as it can be solved numerically using the recently developed interior-point algorithm or be checked using simple algebraic calculation. In addition, the proposed results generalize and improve upon some previous works. Two numerical examples are used to show the effectiveness of the obtained results.

Exponential stability of cellular neural networks with multiple time delays and impulsive effects

In this work, the stability issues of the equilibrium points of the cellular neural networks with multiple time delays and impulsive effects are investigated. Based on the stability theory of Lyapunov-Krasovskii, the method of linear matrix inequality （LMI） and parametrized first-order model transformation, several novel conditions guaranteeing the delaydependent and the delay-independent exponential stabilities are obtained. A numerical example is given to illustrate the effectiveness of our results.

Asymptotical mean square stability of cellular neural networks with random delay

In this paper,the asymptotical mean-square stability analysis problem is considered for a class of cellular neural networks (CNNs) with random delay. Compared with the previous work,the delay is modeled by a continuous-time homogeneous Markov process with a finite number of states. The main purpose of this paper is to establish easily verifiable conditions under which the random delayed cellular neural network is asymptotic mean-square stability. By using some stochastic analysis techniques and Lyapunov-Krasovskii functional,some conditions are derived to ensure that the cellular neural networks with random delay is asymptotical mean-square stability. A numerical example is exploited to show the vadlidness of the established 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.

CONDITIONS OF ASYMPTOTIC STABILITY FOR CELLULAR NEURAL NETWORKS WITH TIME DELAY

In this paper, global asymptotic stability for cellular neural networks with time delay is discussed using a novel Liapunov function. Some novel sufficient conditions for global asymptotic stability are obtained. Those results are simple and practical than those given by P. P. Civalleri, et al., and have a leading importance to design cellular neural networks with time delay.

Stability analysis of delayed cellular neural networks with and without noise perturbation

The stability of a class of delayed cellular neural networks （DCNN） with or without noise perturbation is studied. After presenting a simple and easily checkable condition for the global exponential stability of a deterministic system, we further investigate the case with noise perturbation. When DCNN is perturbed by external noise, the system is globally stable. An important fact is that, when the system is perturbed by internal noise, it is globally exponentially stable only if the total noise strength is within a certain bound. This is significant since the stochastic resonance phenomena have been found to exist in many nonlinear systems.

Stability for Cellular Neural Networks with Delay

The cellular neural networks with delay (DCNN’s) are investigated, and some new sufficient conditions on asymptotical stability of DCNN’s are derived by constructing the Liapunov functional and utilizing M ? matrixand theω?limit set. It is shown that the new conditions are not related to the delayed parameter.

New results on the robust stability analysis of neural networks with discrete and distributed time delays

Delay-dependent robust stability of cellular neural networks with time-varying discrete and distributed time-varying delays is considered. Based on Lyapunov stability theory and the linear matrix inequality （LMIs） technique, delay-dependent stability criteria are derived in terms of LMIs avoiding bounding certain cross terms, which often leads to conservatism. The effectiveness of the proposed stability criteria and the improvement over the existing results are illustrated in the numerical examples.

Exponential stability criteria on neural networks with continuously distributed delays

The exponential stability of a class of neural networks with continuously distributed delays is investigated by employing a novel Lyapunov-Krasovskii functional. Through introducing some free-weighting matrices and the equivalent descriptor form, a delay-dependent stability criterion is established for the addressed systems. The condition is expressed in terms of a linear matrix inequality （LMI）, and it can be checked by resorting to the LMI in the Matlab toolbox. In addition, the proposed stability criteria do not require the monotonicity of the activation functions and the derivative of a time-varying delay being less than 1, which generalize and improve earlier methods. Finally, numerical examples are given to show the effectiveness of the obtained methods.

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 cellular neural networks: an LMI approach

A new sufficient conditions for the global exponential stability of the equilibrium point for delayed cellular neural networks （DCNNs） is presented. It is shown that the use of a more general type of Lyapunov-Krasovskii function enables the derivation of new results for an exponential stability of the equilibrium point for DCNNs. The results establish a relation between the delay time and the parameters of the network. The results are also compared with one of the most recent results derived in the literature.

Delay-dependent Criteria for Robust Stability of Uncertain Switched Hopfield Neural Networks

This paper deals with the problem of delay-dependent robust stability for a class of switched Hopfield neural networks with time-varying structured uncertainties and time-varying delay. Some Lyapunov-KrasoVskii functionals are constructed and the linear matrix inequality （LMI） approach and free weighting matrix method are employed to devise some delay-dependent stability criteria which guarantee the existence, uniqueness and global exponential stability of the equilibrium point for all admissible parametric uncertainties. By using Leibniz-Newton formula, free weighting matrices are employed to express this relationship, which implies that the new criteria are less conservative than existing ones. Some examples suggest that the proposed criteria are effective and are an improvement over previous ones.

Novel delay-dependent stability criteria for neural networks with interval time-varying delay

The problem of delay-dependent asymptotic stability for neurM networks with interval time-varying delay is investigated. Based on the idea of delay decomposition method, a new type of Lyapunov Krasovskii functional is constructed. Several novel delay-dependent stability criteria are presented in terms of linear matrix inequality by using the Jensen integral inequality and a new convex combination technique. Numerical examples are given to demonstrate that the proposed method is effective and less conservative.

Stability analysis of cellular neural networks with time-varying delay

The global asymptotic stability of cellular neural networks with delays is investigated. Three kinds of time delays have been considered. New delay-dependent stability criteria are proposed and are formulated as the feasibility of some linear matrix inequalities, which can be checked easily by resorting to the recently developed interior-point algorithms. Based on the Finsler Lemma, it is theoretically proved that the proposed stability criteria are less conservative than some existing results.

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.