Finite-time H∞ fuzzy control for Markovian Jump stochastic systems

This paper deals with the problems of finite-time stochastic stabilization and finite-time H_∞ control for Markovian Jump stochastic systems via a fuzzy-control approach. The Takagi-Sugeno (T-S) fuzzy model is employed to represent a nonlinear stochastic system with Markovian jump parameters. The purpose of the finite-time stochastic stabilization problem is to design a state feedback fuzzy controller such that the closed-loop fuzzy system is finite-time stochastic stable. In the H_∞ control problem, in addition to the finite-time stochastic stability requirement, a prescribed performance is required to be achieved. Linear matrix inequalities (LMIs) sufficient conditions are developed to solve these problems, respectively. The expressions of desired state feedback fuzzy controllers are given.