A Novel Free-Matrix-Based Summation Inequality for Stability Analysis of Discrete-Time Delayed System

Abstract

This paper introduces an improved stability criterion for discrete-time systems with time-varying delay. A novel summation inequality based on the free-matrix is suggested which considers the augmented vector of the state and its forward difference. Additionally, the proposed summation inequality is employed to derive an improved stability criterion for the discrete-time system with time-varying delay. A new Lyapunov-Krasovskii functional is established for applying the summation lemma to reduce the conservatism of the stability analysis. To verify the effectiveness of the proposed approach, the maximum admissible upper bounds of the proposed method is presented in comparison to existing methods with two numerical examples.