%0 Journal Article
%T A Delay-Dependent Approach to Stability of Uncertain Discrete-Time State-Delayed Systems with Generalized Overflow Nonlinearities
%A V. Krishna Rao Kandanvli
%A Haranath Kar
%J ISRN Computational Mathematics
%D 2012
%R 10.5402/2012/171606
%X This paper addresses the problem of global asymptotic stability of a class of uncertain discrete-time state-delayed systems employing generalized overflow nonlinearities. The systems under investigation involve parameter uncertainties that are assumed to be deterministic and norm bounded. A new computationally tractable delay-dependent criterion for global asymptotic stability of such systems is presented. A numerical example is given to illustrate the effectiveness of the proposed method. 1. Introduction In the implementation of linear discrete systems, signals are usually represented and processed in a finite wordlength format which frequently generates several kinds of nonlinearities, such as overflow and quantization. Such nonlinearities may lead to instability in the designed system. Therefore, the study of stability problem for discrete-time systems with finite wordlength nonlinearities is important not only for its theoretical interest but also for application to practical system design. Many publications [1¨C22] relating to the issue of the global asymptotic stability of discrete-time systems with overflow nonlinearities have appeared. Parameter uncertainties are often introduced in many physical systems as a consequence of variations in system parameters, modeling errors or some ignored factors. Such uncertainties may result in the deterioration of system performance and instability of the system. Time delay is another source of instability for discrete-time systems. They are frequently introduced in many physical, industrial, and engineering systems due to finite capabilities of information processing and signal transmission among various parts of the system. During the past few decades, there has emerged a considerable interest on the stability analysis problems for delayed systems [17¨C21, 23¨C31]. According to the dependence of delay, the available stability criteria for delayed systems can be broadly classified into two types: delay independent and delay dependent. Increasing attention is being paid to delay-dependent stability criteria for delayed systems since they can often provide less conservative results than delay-independent criteria [17, 25, 27]. The problem of establishing delay-dependent criteria for the global asymptotic stability of discrete-time uncertain state-delayed systems with overflow nonlinearities is an important and challenging task. So far, very little attention has been paid for the investigation of this problem [17, 21]. In this paper, we consider the problem of global asymptotic stability of a class of discrete-time
%U http://www.hindawi.com/journals/isrn.computational.mathematics/2012/171606/