Non-fragile control design for interval-valued fuzzy systems against nonlinear actuator faults

Abstract In this paper, we consider the reliable non-fragile H ∞ control design problem for a class of discrete-time interval-valued fuzzy systems with actuator faults. More precisely, the actuator fault model considered in the controller design consists of linear and nonlinear fault terms. The main focus of this paper is to design a non-fragile state feedback controller that is characterized by membership functions described by upper and lower membership functions and nonlinear weighting functions. It should be mentioned that the proposed interval-valued fuzzy system and the controller do not share same membership functions. A novel set of sufficient conditions is obtained by transforming the controller design problem into a multi-objective convex optimization problem based on the linear matrix inequality and the Lyapunov functional approaches, which ensures the robust asymptotic stability of the addressed system with a desired H ∞ performance index. Finally, two numerical examples, including an application-oriented model, mass-spring-damping system are presented to demonstrate the effectiveness of the proposed design technique.