New Design Approach of Robust H∞ Control for Uncertain Fuzzy Markovian Jump Systems

This paper is concerned with the problem of robust Hinfin control for a class of uncertain nonlinear Markovian jump systems described by the Takagi-Sugeno (T-S) fuzzy models. The aim is to find a mode-dependent state feedback controller such that the closed-loop fuzzy jump system is robustly stochastically stable and a prescribed Hinfin performance level is satisfied for all admissible uncertainties. By introducing two free matrix variables, a new sufficient condition for the existence of such a controller is derived in terms of linear matrix inequalities (LMIs). The last numerical example is provided to illustrate the effectiveness of the developed results.