Multi-variance Performance Constrained Robust Fuzzy Control for Fuzzy Model-Based Discrete-time Stochastic Systems

In this paper, the multiple performance problems including the stochastic behaviors, perturbations, and transient behaviors of time response are considered for the discrete-time nonlinear systems. Based on the Takagi-Sugeno fuzzy model, a robust fuzzy controller design method is proposed to achieve the requirements of the above performances. Firstly, the covariance control theory is applied to achieve stability and also suppress the energy of the system under the effects of stochastic behaviors. Secondly, the robust control theory is applied to deal with the perturbations in the system state and input. Thirdly, the pole placement theory is applied to obtain better transient behaviors by locating the closed-loop poles in the given region. Moreover, all the theories are combined into each other such that the multiple performance requirements can be satisfied, simultaneously. To verify the proposed robust fuzzy controller design method, a numerical example for the control of a nonlinear discrete-time stochastic system is provided.