Stability analysis of discrete-time systems with a time-varying delay via improved methods

This paper is concerned with the stability analysis of discrete-time systems with a time-varying delay. The conservatism and computation burden are two important factors to evaluate a stability condition. By taking the relationship of two reciprocally convex parts into consideration, a new combined matrix-separation-based inequality is proposed that involves only a few free matrices. Moreover, an improved matrix-injection-based transformation lemma with the parameter varying within a closed interval is proposed by introducing only one free matrix. By constructing an appropriate Lyapunov–Krasovskii functional and applying the improved methods, a relaxed stability condition is consequently obtained with a small number of decision variables. Two numerical examples are given to show the merits of the proposed methods.