Robust H-infinity fuzzy control for uncertain Markovian jump nonlinear singular systems with wiener process

Abstract

This paper deals with the problems of robust stochastic stabilization and H-infinity 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. 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. In the robust H-infinity control problem, in addition to the stochastic stability requirement, a prescribed performance is required to be achieved. Linear matrix inequality (LMI) sufficient conditions are developed to solve these problems, respectively. The expressions of desired state feedback fuzzy controllers are given. Finally, a numerical simulation is given to illustrate the effectiveness of the proposed method.