An Augmented Lyapunov-Krasovskii Functional Approach to Analyze Stability of T-S Fuzzy Systems With Time-Varying Delay

Abstract

In this paper, we propose an improved delay-and-delay-derivative-dependent stability criterion of T-S fuzzy system with time-varying delay. The criterion is derived by applying an augmented Lyapunov-Krasovskii functional approach together with a canonical Bessel-Legendre inequality, and it is given in the form of linear matrix inequalities. By numerical comparison, we show that the obtained criterion can ensure a lager upper delay bound over some recent published delay-dependent stability criteria and it can be improved by increasing the number of Legendre polynomials.