Passive fuzzy control for ball and beam systems via Takagi-Sugeno fuzzy model with multiplicative noises

This paper proposes a passive fuzzy controller design methodology for stabilization of nonlinear system with external disturbance based on multiplicative noised Takagi-Sugeno fuzzy model and parallel distributed compensation control design. Applying the Itô´s 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. The sufficient conditions derived in this paper belong to the linear matrix inequality forms which can be solved efficiently by convex optimal programming algorithm. Besides, the passivity theory is applied to discuss the effect of external disturbance on system. Finally, a ball and beam system is provided in the example to demonstrate the applications of the proposed fuzzy controller design technique.