Reliable Robust $H∞$ Fuzzy Control for Uncertain Nonlinear Systems With Markovian Jumping Actuator Faults

This paper is concerned with the design of reliable robust $H∞$ fuzzy control for uncertain nonlinear continuous-time systems with Markovian jumping actuator faults. The Takagi and Sugeno fuzzy model is employed to represent an uncertain nonlinear system with Markovian jumping actuator faults. First, based on the parallel distributed compensation (PDC) scheme, a sufficient condition such that the closed-loop fuzzy system is robustly stochastically stable and satisfies a prescribed level of $H∞$-disturbance attenuation is derived. In the derivation process, a stochastic Lyapunov function is used to test the stability and $H∞$ performance of the system. Then, a new improved linear matrix inequality (LMI) formulation is applied to this condition to alleviate the interrelation between the stochastic Lyapunov matrix and system matrices containing controller variables, which results in a tractable LMI-based condition for the existence of reliable and robust $H∞$ fuzzy controllers. A suboptimal fuzzy controller is proposed to minimize the level of disturbance attenuation subject to the LMI constraints. Finally, a simulation example is given to illustrate the effectiveness of the proposed method.