Robust State Feedback H_∞ Control for Discrete-Time Fuzzy System With Random Delays

This paper investigates the problem of robust stabilization for a class of discrete-time Takagi–Sugeno (TS) fuzzy systems via input random delays in control input. The main objective of this paper is to design a state feedback $H∞$ controller. Linear matrix inequality (LMI) approach together with the construction of proper Lyapunov–Krasovskii functional is employed for obtaining delay dependent sufficient conditions for the existence of robust $H∞$ controller. In particular, the effect of both variation range and distribution probability of the time delay is taken into account in the control input. The key feature of the proposed results in this paper is that the time‐varying delay in the control input not only dependent on the bound but also the distribution probability of the time delay. The obtained results are formulated in terms of LMIs which can be easily solved by using the standard optimization algorithms. Finally, a numerical example with simulation result is provided to illustrate the effectiveness of the obtained control law and less conservativeness of the proposed result.