%0 Journal Article
%T Global Exponential Stability of Discrete-Time Neural Networks with Time-Varying Delays
%A S. Udpin
%A P. Niamsup
%J Discrete Dynamics in Nature and Society
%D 2013
%I Hindawi Publishing Corporation
%R 10.1155/2013/325752
%X This paper presents some global stability criteria of discrete-time neural networks with time-varying delays. Based on a discrete-type inequality, a new global stability condition for nonlinear difference equation is derived. We consider nonlinear discrete systems with time-varying delays and independence of delay time. Numerical examples are given to illustrate the effectiveness of our theoretical results. 1. Introduction In recent years, neural networks (NNs) have been investigated extensively due to their broad applications in information processing problems, associative memory, parallel computation, pattern recognition, signal processing, and optimization problems. It is well known that delays are often the sources of instability and oscillation in system. In practical studies, discrete-time systems have been used for a variety of phenomena in electrical networks, genetics, ecological systems, and so forth. Therefore, the stability analysis of discrete-time neural networks (DNNs) with delays has become an important topic of theoretical studies in neural networks; for example, asymptotic stability and exponential stability of neural networks have been studied by many researchers. In [1], the authors have studied robust stability of discrete-time linear-parameter-dependent (LPD) neural networks with time-varying delay. In order to derive stability criteria of discrete-time, one common approach is the use of appropriate inequalities for difference equations. Another approach is the use of Lyapunov stability theory. In [2], the authors have studied global exponential stability of impulsive discrete-time neural networks with time-varying delays, based on some inequality analysis techniques. In [3], the authors have studied new discrete-type inequalities and global stability of nonlinear difference equation. In [4], the authors have studied global exponential stability of discrete-time Hopfield neural networks with variable by using the difference inequality. In [5], the authors have considered the problem of robust stability analysis of generalized neural networks with multiple discrete delays and multiple distributed delays by using the Lyapunov-Krasovskii functional method and the linear matrix inequality technique. In [6], the authors have studied delay-dependent exponential stability criteria for discrete-time nonlinear system with multiple time-varying delays. In this paper, we propose to study global exponential stability of discrete-time neural networks with time-varying delays. In Section 2, we have introduced discrete-time neural networks with
%U http://www.hindawi.com/journals/ddns/2013/325752/