Reliable ${H}_{\infty}$ Fuzzy Control for a Class of Discrete-Time Nonlinear Systems Using Multiple Fuzzy Lyapunov Functions

This brief deals with the problem of reliable H
_infin
fuzzy control for a class of discrete-time nonlinear systems with actuator faults by using multiple fuzzy Lyapunov functions. The Takagi and Sugeno fuzzy model is employed to represent a nonlinear system. A sufficient condition for the existence of reliable H
_infin
fuzzy controllers is given in terms of linear matrix inequalities (LMIs), which can guarantee that the closed-loop fuzzy system is globally asymptotically stable and satisfies different levels of disturbance attenuation for different operating regimes. Furthermore, a suboptimal reliable fuzzy controller is proposed for minimizing the normal level while maintaining acceptable levels in the faulty cases. Finally, it is also demonstrated, through numerical simulations on a discrete-time chaotic system, that the proposed method is effective