Individual state variance constrained fuzzy control for discrete nonlinear stochastic systems

An individual state variance constrained fuzzy controller design methodology is developed in this paper to achieve state variance constraint and passivity constraint for discrete nonlinear multiplicative noised stochastic systems. The discrete nonlinear multiplicative noised stochastic system considered in this paper is represented by the discrete-time Takagi-Sugeno fuzzy model. The proposed fuzzy controller is constructed by the concept of parallel distributed compensation. The sufficient conditions are derived based on the Lyapunov theory. Employing the matrix transformation technique, these sufficient conditions can be expressed in terms of linear matrix inequalities. Finally, the feasibility and validity of the proposed method are illustrated with a numerical simulation example.