Observer-based H∞ fuzzy control design for discrete-time stochastic T-S fuzzy model with multiplicative noise

This paper introduces an observer-based H_infin fuzzy control design method for discrete-time nonlinear systems with multiplicative noise. First, the Takagi-Sugeno (T-S) fuzzy model is employed to approximate a nonlinear discrete-time system with multiplicative noise. Secondly, the stability conditions are derived via Lyapunov function to analyze the stability and H_infin performance of system. Thirdly, the standard two-step method is adopted to separately obtain the controller gain matrices and the observer gain matrices by solving two sets of linear matrix inequalities (LMIs). Finally, a numerical simulation is given to demonstrate the application of the proposed approach.