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.

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.

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.

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.

GLOBAL ASYMPTOTIC STABILITY CONDITIONS OF DELAYED NEURAL NETWORKS

Utilizing the Liapunov functional method and combining the inequality of matrices technique to analyze the existence of a unique equilibrium point and the global asymptotic stability for delayed cellular neural networks (DCNNs), a new sufficient criterion ensuring the global stability of DCNNs is obtained. Our criteria provide some parameters to appropriately compensate for the tradeoff between the matrix definite condition on feedback matrix and delayed feedback matrix. The criteria can easily be used to design and verify globally stable networks. Furthermore,the condition presented here is independent of the delay parameter and is less restrictive than that given in the references.

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.

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.

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.

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 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.

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.

Bifurcation and Chaos in Delayed Cellular Neural Network Model

This paper deals with control of chaotic behavior of a delayed Cellular Neural Network (DCNN) model which is a one-dimensional regular array of four cells with continuous activation function. We investigate different dynamical behaviors including limit cycle, torus, and chaos for different range of weight parameters of the system. Regarding synaptic weight as parameter, Hopf bifurcations are obtained in the system without delay. In the delayed model condition for the Global asymptotic stability of the equilibrium point is presented. Numerical simulation and results are given to show the role of delay in chaos control of the CNNs.

Global Asymptotic Stability of Neural Networks with Time Delay

The global asymptotic stability problem of Cellular neural networks with delay is investigated.A new stability condition is presented based on Lyapunov-Krasovskii method,which is dependent on the size of delay.The result is given in the form of LMI,and the admitted upper bound of the delay can be obtained easily.The time delay dependent and independent results can be obtained,which include some results in the former literature.Finally,a numerical example is given to illustrate the effectiveness of the main results.

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.

Exponential stability and periodic solutions of delayed cellular neural networks

A set of criteria are presented for the global exponential stability and the existence of periodic solutions of delayed cellular neural networks (DCNNs) by constructing suitable Lyapunov function-als, introducing many parameters qij* , rij* , qij, rij∈ R and wi】0 (i, j = 1, 2, …, n) and combining them with the elementary inequality 2ab≤a2 + b2 technique. These criteria have important significance in the design and applications of globally stable DCNNs and periodic oscillatory DCNNs. In addition, the results in literature are extended and improved. Two examples are given to illustrate the theory.

On stability of delayed cellular neural networks with sigmoid output functions

In this paper a sufficient condition is presented to ensure the complete stability of delayed CNNs. Such a condition establishes a relation between the time delay and the parameters of the networks. Specially, for a given output function f(x) = tanh(x), we address a sufficient condition to ensure absolute convergence of system state.

Exponential convergence and stability of delayed fuzzy cellular neural networks with time-varying coefficients

In this paper, the dynamic behaviors of fuzzy cellular neural networks （FCNNs） with time-varying coefficients and delays are considered. Some criteria are established to ensure the exponential convergence or exponential stability of such neural networks. The effectiveness of obtained results is illustrated by a numerical example.

PERIODIC SOLUTIONS TO FUZZY CELLULAR NEURAL NETWORKS WITH DISTRIBUTED DELAYS

In this paper, a class of fuzzy cellular neural networks with distributed delays is discussed. By employing fixed point theorem and inequality techniques, some sufficient conditions are obtained to ensure the existence and global exponential stability of periodic solutions to the systems. Without assuming the global Lipschitz conditions of activation functions, our results are novel and reduce the limitation of previous known results. Moreover, an example is given to illustrate the effectiveness of our results.

W^(1,2)(Ω)-and X^(1,2)(Ω)-stability of reactiondiffusion cellular neural networks with delay

With Poincare＇s inequality and auxiliary function applied in a class of retarded cellular neural networks with reaction-diffusion, the conditions of the systems＇ W^1,2（Ω）-exponential and X^1,2（Ω）-asmptotic stability are obtained. The stability conditions containing diffusion term are different from those obtained in the previous papers in their exponential stability conditions. One example is given to illustrate the feasibility of this method in the end.