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 meansquare sense with anH
∞ 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.