Stability analysis of discrete-time systems with time-varying delays: generalized zero equalities approach

Abstract

Summary This paper suggests a generalized zero equality lemma for summations, which leads to making a new Lyapunov–Krasovskii functional with more state terms in the summands and thus applying various zero equalities for deriving stability criteria of discrete-time systems with interval time-varying delays. Also, using a discrete-time counter part of Wirtinger-based integral inequality, Jensen inequality, and a lower bound lemma for reciprocal convexity, the forward difference of the Lyapunov–Krasovskii functional is bounded by the combinations of various state terms including not only summation terms but also their interval-normalized versions, which contributes to making the criteria less conservative. Numerical examples show the improved performance of the criteria in terms of maximum delay bounds. Copyright © 2016 John Wiley & Sons, Ltd.