Further results on stability analysis of discrete-time systems with time-varying delays via the use of novel convex combination coefficients

Abstract

This paper focuses on deriving an improved stability criterion for discrete time-delay systems via a Lyapunov–Krasovskii functional approach that takes advantage of triple summation terms. To this end, novel convex combination coefficients coupled with second-order time-varying delay terms are introduced, and the corresponding reciprocally convex approach is established with the use of the minimal number of slack matrix variables. Finally, three numerical examples are provided to illustrate the effectiveness of the proposed method, with particular regard to robustness and H∞ performance.