Stability criteria for linear discrete-time systems with interval-like time-varying delay

Abstract

This paper is concerned with the stability problem for a class of uncertain linear discrete-time systems with time-varying delay. The delay is of an interval-like type, which means that both lower and upper bounds for the time-varying delay are available. The uncertainty under consideration is norm-bounded uncertainty. Based on Lyapunov-Krasovskii functional approach, delay-dependent stability criteria are obtained using a sum inequality which is first introduced and plays an important role in deriving stability conditions. The criteria are formulated in the form of linear matrix inequalities (LMIs). A numerical example is given to show the effectiveness of the proposed criteria.