Reliable $H_\infty$ Control for Discrete-Time Fuzzy Systems With Infinite-Distributed Delay

In this paper, the problem of reliable H_∞ control is investigated for discrete-time Takagi-Sugeno (T-S) fuzzy systems with infinite-distributed delay and actuator faults. A discrete-time homogeneous Markov chain is used to represent the stochastic behavior of actuator faults. In terms of a stochastic fuzzy Lyapunov functional, a sufficient condition is proposed to ensure that the resultant closed-loop system is exponentially stable in the mean-square sense with an H_∞ performance index. Based on the derived condition, the reliable H_∞ control problem is solved, and an explicit expression of the desired controller is also given. The case of no failure in the actuator is also considered. A numerical example is given to demonstrate that our results are effective and less conservative.