Improved stability and stabilisation criteria for discrete time‐delay systems via a novel double summation inequality

Abstract

This study focuses on the problem of stability analysis and stabilisation for discrete time-delay systems. A new type of augmented Lyapunov-Krasovskii functional (LKF) is proposed to derive less conservative stability and stabilisation conditions. A novel inequality is developed to handle more general double summation terms which arise from the forward difference of augmented LKF. Several zero equalities are introduced to further relax the existing results. Using some advanced convexificator techniques, the derived stability and stabilisation conditions are presented in terms of linear matrix inequalities. Several numerical examples are provided to demonstrate the advantage of the proposed approach.