Robust H infinity Reliable Fuzzy Control for Markovian Jump Nonlinear Singular Systems

This paper deals with the problem of robust H_∞ reliable control 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 objective is to design a state feedback fuzzy controller such that, for all admissible uncertainties as well as normal and different actuator failure cases, the resulting closed-loop system is robustly stochastically stable while satisfying a prescribed performance constraint. Based on linear matrix inequality (LMI) techniques, stochastic Lyapunov function method is adopted to establish sufficient condition of existence and design method of robust H_∞ reliable fuzzy controller in terms of stability theory for stochastic differential equations.