LMI-based fuzzy controller design with minimum upper bound input energy and state variance constraints for discrete fuzzy stochastic systems

Abstract

In this paper, a fuzzy controller design problem is considered for the discrete-time Takagi-Sugeno (T-S) fuzzy stochastic systems. The main purpose of this paper is to provide a systematic fuzzy controller design procedure for the discrete-time nonlinear stochastic systems, which are modeled by the T-S type fuzzy systems. A methodology is developed to find the discrete-time fuzzy controllers for minimizing upper bound control input energy and achieving state variance constraints for discrete-time T-S fuzzy stochastic systems. It is shown that the present approach can be used to solve the linear feedback control gains for each rule of the T-S fuzzy controllers using the Linear Matrix Inequality (LMI) technique. Finally, we apply the proposed controller design method to control a truck-trailer system to show the utility of the present approach.