Robust fuzzy control for uncertain Markovian jump nonlinear singular systems

This paper deals with the problem of robust stochastic stabilization for Markovian jump nonlinear singular systems with Wiener process via a fuzzy-control approach. The Takagi-Sugeno (T-S) fuzzy model is employed to represent a nonlinear singular system with norm-bounded parameter uncertainties and Markovian jump parameters. The purpose of the robust stochastic stabilization problem is to design a state feedback fuzzy controller such that the closed-loop fuzzy system is robustly stochastically stable for all admissible uncertainties. Linear matrix inequality (LMI) sufficient conditions are developed to solve the above problem. The expression of desired state feedback fuzzy controller is given. Finally, a numerical simulation is given to illustrate the effectiveness of the proposed method.