%0 Journal Article
%T Delay-Partitioning Approach to Stability of Linear Discrete-Time Systems with Interval-Like Time-Varying Delay
%A Priyanka Kokil
%A V. Krishna Rao Kandanvli
%A Haranath Kar
%J International Journal of Engineering Mathematics
%D 2013
%R 10.1155/2013/291976
%X This paper is concerned with the problem of global asymptotic stability of linear discrete-time systems with interval-like time-varying delay in the state. By utilizing the concept of delay partitioning, a new linear-matrix-inequality-(LMI-) based criterion for the global asymptotic stability of such systems is proposed. The proposed criterion does not involve any free weighting matrices but depends on both the size of delay and partition size. The developed approach is extended to address the problem of global asymptotic stability of state-delayed discrete-time systems with norm-bounded uncertainties. The proposed results are compared with several existing results. 1. Introduction A source of instability for discrete-time systems is time delay which inevitably exists in various engineering systems. In many applications, time delays are unavoidable and must be taken into account in a realistic system design, for instance, chemical processes, echo cancellation, local loop equalization, multipath propagation in mobile communication, array signal processing, congestion analysis and control in high speed networks, neural networks, and long transmission line in pneumatic systems [1每6]. The stability analysis of time-delay systems has received considerable attention during the last two decades [3每7]. According to dependence of delay, the existing stability criteria are generally classified into two categories: delay-dependent criteria and delay-independent criteria. It is well known that delay-independent stability criteria are usually more conservative than the delay-dependent ones, especially if the size of time delay is small [6每10]. Therefore, much attention has been paid in recent years to the study of delay-dependent stability criteria. A number of publications relating to the delay-dependent stability of continuous time-delay systems have appeared (see, e.g., [10每17] and the references cited therein). In contrast, less attention has been paid to studying the problem of stability of discrete time-delay systems. Several delay-dependent criteria for the stability of discrete-time systems have appeared [3, 6, 7, 18, 19]. Reference [7] (see [6] also) presents a novel delay-dependent linear-matrix-inequality-(LMI-) based condition for the global asymptotic stability of linear discrete-time systems with interval-like time-varying delay. The criteria proposed in [6, 7] are less conservative with smaller numerical complexity than [19每23]. The delay partitioning approach has been efficiently applied in [24每30] to the stability analysis of systems with
%U http://www.hindawi.com/journals/ijem/2013/291976/