Stabilization for Markovian jump nonlinear systems with partly unknown transition probabilities via fuzzy control

Abstract

Abstract This paper is concerned with the stability and stabilization problems for a class of nonlinear systems with Markovian jump parameters. The Takagi–Sugeno (T–S) fuzzy model is employed to represent the Markovian jump nonlinear systems with partly unknown transition probabilities. In contrast with the certain or uncertain transition probabilities investigated recently, the concept of partly unknown transition probabilities does not need any knowledge of the unknown elements. Some sufficient conditions for stochastic stability and stabilization conditions with a mode-dependent fuzzy controller are derived for the Markovian jump fuzzy systems in terms of linear matrix inequalities (LMIs). A numerical example is provided to illustrate the design developed in this paper.