Robust stability of linear uncertain discrete-time systems with interval time-varying delay

Abstract

This paper presents a robust stability problem for linear uncertain discrete-time systems with interval time-varying delay and norm-bounded uncertainties. First, a necessary and sufficient stability condition is obtained by employing a well-known lifting method and switched system approach for nominal discrete-time delay systems. Both the stability method of checking the characteristic values inside the unit circle and a Lyapunov function-based stability result are taken into consideration. Second, a simple Lyapunov--Krasovskii functional (LKF) is selected, and utilizing a generalized Jensen sum inequality, a sufficient stability condition is presented in the form of linear matrix inequalities. Third, a novel LKF is proposed together with the use of a convexity approach in the LKF. Finally, the proposed method is extended to the case when the system under consideration is subject to norm-bounded uncertainties. Three numerical examples are introduced to illustrate the effectiveness of the proposed approach, along with some numerical comparisons.