Performance constrained fuzzy control for discrete nonlinear stochastic systems with multiplicative noises and perturbations

A performance constrained fuzzy controller design problem for discrete-time perturbed nonlinear stochastic systems with multiplicative noises is studied in this paper. The purpose of this approach is to design fuzzy controllers to simultaneously achieve variance and passivity constraints. Some sufficient conditions are derived based on the Lyapunov theory. These sufficient conditions are developed in term of the linear matrix inequality forms, thus they can be solved by the convex optimal programming algorithm. Besides, the proposed fuzzy controllers are constructed by using the technique of parallel distributed compensation. Finally, a numerical simulation example is given to show the effectiveness and applicability of the proposed fuzzy control methodology.