Fuzzy control with robust and passive properties for discrete-time Takagi-Sugeno fuzzy systems with multiplicative noises

This paper deals with the problem of robust fuzzy control for uncertain passive discrete-time non-linear stochastic systems with multiplicative noise. In this paper the non-linear stochastic system is represented by a Takagi-Sugeno fuzzy model. Using that approach the concept of parallel distributed compensation is applied to construct the fuzzy controller. Sufficient stability conditions are derived in terms of a linear matrix inequality by applying the Lyapunov theory. In addition, the passivity theory and robust technique are used to guarantee strict input passivity and robust asymptotical stability of the closed-loop system with admissible parameter uncertainties. Finally, a numerical example concerning the control of a truck-trailer system is provided to demonstrate the validity of the proposed fuzzy controller design method.