Reliable observer-based H∞ control for discrete-time fuzzy systems with time-varying delays and stochastic actuator faults via scaled small gain theorem

This paper is concerned with the reliable observer-based H∞H∞ control problem for discrete-time Takagi–Sugeno (T–S) fuzzy systems with time-varying delay and stochastic actuator faults based on input–output approach. A discrete-time homogeneous Markov chain is used to represent the stochastic behavior of actuator faults. First, the discrete-time T–S fuzzy system is transformed into the form of interconnection of two subsystems by employing a new model transformation for the delayed state variables. Furthermore, a sufficient condition on discrete-time T–S fuzzy systems with time-varying delay and actuator faults, which guarantees the corresponding closed-loop system to be stochastically stable and preserves a guaranteed H∞H∞ performance, is derived by employing the scaled small gain theorem. Meanwhile, the solvability condition for the reliable observer-based H∞H∞ control is also established, by which the reliable H∞H∞ fuzzy controller can be solved as linear matrix inequalities (LMIs). Finally, a numerical example is provided to demonstrate the effectiveness of the proposed approach.