Reliable H2 control for discrete-time T-S fuzzy bilinear systems

This paper is concerned with the problem of reliable H₂ control for discrete-time T-S fuzzy bilinear systems with actuator faults. A discrete-time homogeneous Markov chain is used to represent the stochastic behavior of actuator faults. Based on a stochastic fuzzy Lyapunov function, two improved stability conditions are proposed to ensure that the resultant closed-loop system is exponentially stable in the mean-square sense with an H₂ performance index. It is shown the 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) is proposed to solve the nonlinear minimization problem. Finally, an illustrative example is provided to demonstrate the effectiveness of the results proposed in this paper.