A novel Lyapunov-Krasovskii functional approach to stability and stabilization for T-S fuzzy systems with time delay

Abstract This paper is concerned with the problem of the stability and stabilization for continuous-time Takagi–Sugeno(T–S) fuzzy systems with time delay. A novel Lyapunov–Krasovskii functional which includes fuzzy line-integral Lyapunov functional and membership-function-dependent Lyapunov functional is proposed to investigate stability and stabilization of T–S fuzzy systems with time delay. In addition, switching idea which can avoid time derivative of membership functions is introduced to deal with derivative term. Relaxed Wirtinger inequality is employed to estimate integral cross term. Sufficient stability and stabilization criteria are derived in the form of matrix inequalities which can be solved using the switching idea and LMI method. Several numerical examples are given to demonstrate the advantage and effectiveness of the proposed method by comparing with some recent works.

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