Observer-Based Reliable $$\mathrm H_2$$ Control for Discrete-Time T-S Fuzzy Bilinear Systems with Infinite Distributed Delays

This paper is concerned with the problem of reliable \(\mathrm H_2\) control for discrete-time T-S fuzzy bilinear systems with actuator faults and infinite-distributed delays. A discrete-time homogeneous Markov chain is used to represent the stochastic behavior of actuator faults. Based on a stochastic fuzzy Lyapunov function, the fuzzy observer-based controllers are designed for T-S fuzzy bilinear delay systems, two improved stability conditions are proposed to ensure that the resultant closed-loop system is exponentially stable in the mean-square sense with an \(\mathrm H_2\) performance index. It is shown the fuzzy observer-based controller can be obtained by solving a set of nonlinear minimization problem involving linear matrix inequalities (LMIs) constraints. An iterative algorithm making use of sequential linear programming matrix method (SLPMM) to derive a single-step LMI condition for fuzzy observer-based control design. Finally, an illustrative example is provided to demonstrate the effectiveness of the results proposed in this paper.