Reliablerm HᵢnftyFuzzy Control for Continuous-Time Nonlinear Systems With Actuator Failures

This paper is concerned with the design of reliable <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Hᵢnfty</tex> fuzzy controllers for continuous-time nonlinear systems with actuator failures. The Takagi and Sugeno fuzzy model is employed to represent a nonlinear system. The objective is to find a stabilizing state-feedback fuzzy controller such that the nominal <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Hᵢnfty</tex> performance is optimized while satisfying a prescribed <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Hᵢnfty</tex> performance constraint in the actuator failure cases. Based on the linear matrix inequality (LMI) techniques, two efficient methods for the design of a suboptimal reliable <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Hᵢnfty</tex> fuzzy controller are proposed. Different Lyapunov functions are used during the design for the nominal and actuator failure cases, which lead to a less conservative controller design. In the first method, a single Lyapunov function is used for the actuator failure cases. The second method adopts a parameter-dependent Lyapunov function for the actuator failure cases, which further reduces the conservatism of the design. Finally, numerical simulations on the chaotic Rossler system are given to illustrate the effectiveness of the proposed design methods.