Approaches to T–S Fuzzy-Affine-Model-Based Reliable Output Feedback Control for Nonlinear Itô Stochastic Systems

This paper deals with the problem of reliable and robust <inline-formula><tex-math notation="LaTeX">$\mathscr {H}_{\infty }$</tex-math></inline-formula> static output feedback (SOF) controller synthesis for continuous-time nonlinear stochastic systems with actuator faults. The nonlinear stochastic plant is expressed by an Itô-type Takagi–Sugeno fuzzy-affine model with parametric uncertainties, and a Markov process is employed to model the occurrence of actuator fault. The purpose is to design an admissible piecewise SOF controller, such that the resulting closed-loop system is stochastically stable with a prescribed disturbance attenuation level in an <inline-formula> <tex-math notation="LaTeX">$\mathscr {H}_{\infty }$</tex-math></inline-formula> sense. Specifically, based on a Markovian Lyapunov function combined with Itô differential formula, S-procedure, and some matrix inequality convexification procedures, two new approaches to the reliable SOF controller analysis and synthesis are proposed for the underlying stochastic fuzzy-affine systems. It is shown that the existence of desired reliable controllers is fully characterized in terms of strict linear matrix inequalities. Finally, simulation examples are presented to illustrate the effectiveness and advantages of the developed methods.