Reliable <formula formulatype="inline"><tex>${H}_{\infty}$</tex></formula> Fuzzy Control for a Class of Discrete-Time Nonlinear Systems Using Multiple Fuzzy Lyapunov Functions

Abstract

This brief deals with the problem of reliable H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">infin</sub> 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 <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">infin</sub> 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