Observer-based fuzzy control design for discrete-time T-S fuzzy bilinear stochastic systems with infinite-distributed delays

This paper is concerned with the problem of observer-based fuzzy control design for discrete-time T-S fuzzy bilinear stochastic systems with infinite-distributed delays. Based on the piecewise quadratic Lyapunov functional (PQLF), the fuzzy observer-based controllers are designed for T-S fuzzy bilinear stochastic systems. It is shown that the stability in the mean square for discrete T-S fuzzy bilinear stochastic systems can be established if there exists a set of PQLF which can be constructed and 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 makes 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.