Passive fuzzy controller design for nonlinear systems with multiplicative noises

This paper proposes a passive fuzzy controller design methodology for nonlinear system with multiplicative noises. Applying the Itôʹs formula and the sense of mean square, the sufficient conditions are developed to analyze the stability and to design the controller for stochastic nonlinear systems which are represented by the Takagi–Sugeno (T–S) fuzzy models. The sufficient conditions derived in this paper belong to the Linear Matrix Inequality (LMI) forms which can be solved by the convex optimal programming algorithm. Besides, the passivity theory is applied to discuss the effect of external disturbance on system. Finally, some numerical simulation examples are provided to demonstrate the applications of the proposed fuzzy controller design technique.