Improved Delay-and-Its-derivative-Dependent Stability and Stabilization Conditions for T-S Fuzzy Systems with Time-Delay

Abstract

This paper proposes some improved delay-dependent stability and stabilization conditions of T-S fuzzy system with time-delay. An augmented Lyapunov-Krasovskii functional (LKF) plus the inequalities such as a Bessel-Legendre (B-L) inequality and a reciprocally convex inequality is constructed to derive these conditions by means of linear matrix inequalities. Different from the existing LKFs, the proposed LKF involves more state variables in an augmentation form based on the application of a canonical B-L inequality. By two numerical examples, it shows that the obtained stability condition can ensure a lager upper bound of delay comparing with some existing conditions, the increasing number of Legendre polynomials in the stability condition can reduce conservatism, and the design result is effective in stabilization.