State and static output feedback control of singular Takagi–Sugeno fuzzy systems with time-varying delay via proportional plus derivative feedback

Abstract

This paper investigates the problems of state and static output feedback control for a class of singular Takagi–Sugeno fuzzy systems with time-varying delay. Two kinds of controllers are considered: one is the proportional plus derivative state feedback controller, the other is the proportional plus derivative static output feedback controller. The augmented Lyapunov–Krasovskii functional is chosen to analyze the stabilization of the considered system and the sufficient conditions are proposed based on the Lyapunov stability theory. In order to solve the controller gains, two iterative algorithms are built. Two persuasive examples are given to show the effectiveness of our methods.