In this paper, we present the stability criteria, sufficient conditions that guarantee the robust stability of linear structured or unstructured variation of discrete time-delay systems subjected to the given bounds of nonlinear function. Both single and composite nonlinear discrete systems with multiple time delays are considered and each of these results is expressed by a succinct scalar inequality and independent of delay time.
KEYWORDS robustness; nonlinear; discrete-time; time-delay
1. Introduction
In recent years the stability and stabilization of continuous time-delay systems have received considerable attention because delay is encountered in various engineering systems and its existence is frequently a source of instability. The stability criteria for continuous time-delay systems, expressed by concise inequalities, have been proposed by some authors.
Regarding the robust analysis of linear systems, some author^^-^ present several sufficient conditions that guarantee the robust stability of uncertain continuous time-delay systems subjected to parametric perturbations. On the other hand, much effort7-' has been geared towards solving the robustness problems of discrete-time systems. The robust analysis and stabilization of linear discrete time-delay systems has been presented by many authors. '*-I3 The D-stability analysis for discrete systems with time-delay, which locate all the poles inside a specific disk, has also been discussed. 14~15 In this paper, we present several sufficient conditions that guarantee the robust stability of nonlinear discrete systems with multiple time delays.
The nonlinear discrete time-delay systems with the general uncertain terms accounting for linear time-invariant and nonlinear time-varying perturbations are treated here. In this paper, we assume that the bounds of nonlinear parametric perturbation are given, then discuss the robustness of linear structured or unstructured perturbations. Of course, the results obtained are also applicable to discrete time-delay systems suffering linear time-varying perturbations. The
This paper was recommended for publication by editor A . lsidori