Stability and Stabilization of Discrete-Time T–S Fuzzy Systems With Time-Varying Delay via Cauchy–Schwartz-Based Summation Inequality

Abstract

This paper proposes new stability and stabilization conditions for discrete-time fuzzy systems with time-varying delays. By constructing a suitable Lyapunov–Krasovskii functional and introducing a new summation inequality based on the inequality of Cauchy–Schwartz form, which enhances the feasible region of the stability criterion for discrete-time systems with time-varying delay, a stability criterion for such systems is established. In order to show the effectiveness of the proposed inequality, which provides more tight lower bound of a summation term of quadratic form, a delay-dependent stability criterion for such systems is derived within the framework of linear matrix inequalities, which can be easily solved by various effective optimization algorithms. Going one step forward, the proposed inequality is applied to a stabilization problem in discrete-time fuzzy systems with time-varying delays. The advantages of the proposed stability and stabilization criteria are illustrated via two numerical examples.