Reliable Output Feedback Control of Discrete-Time Fuzzy Affine Systems With Actuator Faults

TLDR: It is shown that by invoking the redundancy properties induced by the descriptor formulation, combined with some convexifying techniques, the existence of the desired reliable controller can be explicitly determined by the solution of a convex optimization problem.

Abstract: This article studies the robust and reliable $\mathscr {H}_{\infty }$ static output feedback (SOF) control for nonlinear systems with actuator faults in a descriptor system framework. The nonlinear plant is characterized by a discrete-time Takagi-Sugeno (T-S) fuzzy affine model with parameter uncertainties, and the Markov chain is utilized to describe the actuator-fault behaviors. Specifically, by adopting a state-output augmentation approach, the original system is firstly reformulated into the descriptor fuzzy affine system. Based upon a novel piecewise Markovian Lyapunov function (LF), the $\mathscr {H}_{\infty }$ performance analysis condition for the underlying system is then presented, and furthermore the robust and reliable SOF controller synthesis is carried out. It is shown that by invoking the redundancy properties induced by the descriptor formulation, combined with some convexifying techniques, the existence of the desired reliable controller can be explicitly determined by the solution of a convex optimization problem. Finally, simulation studies are applied to confirm the effectiveness of the developed method.