Global asymptotic stability and global exponential stability of delayed cellular neural networks

In this brief, many novel theorems and corollaries are presented regarding the global asymptotic stability and global exponential stability of cellular neural networks with constant and variable time delays. The stability conditions in the new results improve and generalize existing ones. Several examples are discussed to compare the new results with the existing ones.     

Global exponential stability and periodicity of recurrent neural networks with time delays

In this paper, the global exponential stability and periodicity of a class of recurrent neural networks with time delays are addressed by using Lyapunov functional method and inequality techniques. The delayed neural network includes the well-known Hopfield neural networks, cellular neural networks, and bidirectional associative memory networks as its special cases. New criteria are found to ascertain the global exponential stability and periodicity of the recurrent neural networks with time delays, and are also shown to be different from and improve upon existing ones.     

神经网络指数稳定性分析及收敛率估计

该文通过李雅普诺夫直接方法,研究了一类 Hopfield神经网络平衡点的存在性、唯一性与指数稳定性。文中假设神经网络系统的激励函数为单调增Lipschitz连续函数,在自反馈项为非线性函数的条件下,研究其指数稳定性,同时给出了收敛率估计式。     

Global asymptotic stability and global exponential stability of neural networks with unbounded time-varying delays

This brief studies the global asymptotic stability and the global exponential stability of neural networks with unbounded time-varying delays and with bounded and Lipschitz continuous activation functions. Several sufficient conditions for the global exponential stability and global asymptotic stability of such neural networks are derived. The new results given in the brief extend the existing relevant stability results in the literature to cover more general neural networks.     

Robust passivity analysis for discrete-time recurrent neural networks with mixed delays

This article considers the robust passivity analysis for a class of discrete-time recurrent neural networks (DRNNs) with mixed time-delays and uncertain parameters. The mixed time-delays that consist of both the discrete time-varying and distributed time-delays in a given range are presented, and the uncertain parameters are norm-bounded. The activation functions are assumed to be globally Lipschitz continuous. Based on new bounding technique and appropriate type of Lyapunov functional, a sufficient condition is investigated to guarantee the existence of the desired robust passivity condition for the DRNNs, which can be derived in terms of a family of linear matrix inequality (LMI). Some free-weighting matrices are introduced to reduce the conservatism of the criterion by using the bounding technique. A numerical example is given to illustrate the effectiveness and applicability.     

New results for exponential stability of delayed cellular neural networks

This brief presents new sufficient conditions for the global exponential stability of the equilibrium point for delayed cellular neural networks (DCNNs). It is shown that the use of a more general type of Lyapunov-Krasovskii functional enables us to derive new results for 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.     

动态热稳定望远镜腔的充分必要条件

本文利用g~′-、g~*-参数等价腔并将输出镜上光斑半径表为归一化光焦度D_n和A参数的形式,首次推出了基模动态热稳定望远镜腔的充分必要条件,同时还分别得出了动态热稳定望远镜腔的归一化光焦度D_n、热焦距f和g_1~*、g_2~*参数的解析表示式.本工作所得结果易于推广用于含有多个透镜(其中有一个是热透镜)的多元件腔的一般情况.     

Delay-dependent exponential stability of delayed neural networks with time-varying delay

In this brief, free-weighting matrices are employed to express the relationship between the terms in the Leibniz-Newton formula; and based on that relationship, a new delay-dependent exponential-stability criterion is derived for delayed neural networks with a time-varying delay. Two numerical examples demonstrate the improvement this method provides over existing ones.     

Global robust stability of a class of discrete-time interval neural networks

This paper is concerned with global robust stability of a general class of discrete-time interval neural networks which contain time-invariant uncertain parameters with their values being unknown but bounded in given compact sets. We first introduce the concept of diagonally constrained interval neural networks and present a necessary and sufficient condition for global robust stability of the interval networks regardless of the bounds of nondiagonal uncertain parameters of state feedback and connection weight matrices. Then we extend the result to general interval neural networks. Finally, simulation results illustrate the characteristics of the main results.     

Novel global asymptotic stability criteria for delayed cellular neural networks

This brief provides improved conditions for the existence of a unique equilibrium point and its global asymptotic stability of cellular neural networks with time delay. Both delay-dependent and delay-independent conditions are obtained by using more general Lyapunov-Krasovskii functionals. These conditions are expressed in terms of linear matrix inequalities, which can be checked easily by recently developed standard algorithms. Examples are provided to demonstrate the reduced conservatism of the proposed criteria by numerically comparing with those reported recently in the literature.     

General necessary conditions for input-output stability

We consider multiple-input multiple-output linear time-invariant feedback systems with unity feedback. For both the continuous-time and the discrete-time case, we show that recently derived sufficient conditions for input-output stability are necessary and, in fact, under much more general conditions.     

Sufficient conditions for stability of multidimensional discrete systems

A number of simple conditions equal to the number of monomials in the denominator polynomial of the transfer function of a discrete multidimensional system, are each shown to be sufficient for the multidimensional part of the stability test for such causal systems.     

Sufficient conditions for global homeomorphism of piecewise linear functions

Sufficient conditions for the existence of unique solutions of piecewise linear functions are derived. They require that a certain set of cofactors of each region around a corner point should have the same sign.     

Global asymptotic and robust stability of recurrent neural networks with time delays

In this paper, two related problems, global asymptotic stability (GAS) and global robust stability (GRS) of neural networks with time delays, are studied. First, GAS of delayed neural networks is discussed based on Lyapunov method and linear matrix inequality. New criteria are given to ascertain the GAS of delayed neural networks. In the designs and applications of neural networks, it is necessary to consider the deviation effects of bounded perturbations of network parameters. In this case, a delayed neural network must be formulated as a interval neural network model. Several sufficient conditions are derived for the existence, uniqueness, and GRS of equilibria for interval neural networks with time delays by use of a new Lyapunov function and matrix inequality. These results are less restrictive than those given in the earlier references.     

Bidirectional recurrent neural networks

In the first part of this paper, a regular recurrent neural network (RNN) is extended to a bidirectional recurrent neural network (BRNN). The BRNN can be trained without the limitation of using input information just up to a preset future frame. This is accomplished by training it simultaneously in positive and negative time direction. Structure and training procedure of the proposed network are explained. In regression and classification experiments on artificial data, the proposed structure gives better results than other approaches. For real data, classification experiments for phonemes from the TIMIT database show the same tendency. In the second part of this paper, it is shown how the proposed bidirectional structure can be easily modified to allow efficient estimation of the conditional posterior probability of complete symbol sequences without making any explicit assumption about the shape of the distribution. For this part, experiments on real data are reported     

A comment on "Globally exponential stability of neural networks with variable delays"

For original paper by Jiye Zhang see IEE Transactions on Circuits & Systems I, vol. 50, No.2, p.288-90, Feb. 2003.     

Global exponential convergence of multitime-scale neural networks

In this paper, we investigate the convergence and stability of a neural network model with different time scales, which models the activity of cortical cognitive maps. We provide a theoretic condition for global exponential convergence of the solutions of the network, which is proved weaker than some existing results in the literature. We also introduce time-varying delays with less constraints into the neural network model and derive a general stability condition for the delay network.     

A unifying proof of global asymptotical stability of neural networks with delay

We present some new global stability results of neural networks with delay and show that these results generalize recently published stability results. In particular, several different stability conditions in the literature which were proved using different Lyapunov functionals are generalized and unified by proving them using the same Lyapunov functional. We also show that under certain conditions, reversing the directions of the coupling between neurons preserves the global asymptotical stability of the neural network.     

An analysis of global asymptotic stability of delayed Cohen-Grossberg neural networks via nonsmooth analysis

In this paper, using a method based on nonsmooth analysis and the Lyapunov method, several new sufficient conditions are derived to ensure existence and global asymptotic stability of the equilibrium point for delayed Cohen-Grossberg neural networks. The obtained criteria can be checked easily in practice and have a distinguished feature from previous studies, and our results do not need the smoothness of the behaved function, boundedness of the activation function and the symmetry of the connection matrices. Moreover, two examples are exploited to illustrate the effectiveness of the proposed criteria in comparison with some existing results.     

Network restoration using recurrent neural networks

In this article, a method is proposed for network restoration using a centralized, static restoration after failure, where the restoration initiated at the local node or at the source uses a hybrid strategy. © 1998 John Wiley & Sons, Ltd.