H_∞ model approximation for discrete-time Takagi-Sugeno fuzzy systems with Markovian jumping parameters

This paper is concerned with the H_∞ model approximation problem for a class of discrete-time Takagi-Sugeno (T-S) fuzzy Markov jump systems. The systems involve stochastic disturbances and nonlinearities that can be described by T-S fuzzy models. The problem to be solved in the paper is to find a reduced-order model, which is able to approximate the original T-S fuzzy Markov jump system with comparatively small and acceptable errors. Specifically, the corresponding error system is guaranteed to be asymptotically stable in the mean square with a prescribed H_∞ performance index. By using convex optimization approach and projection approach, respectively, sufficient conditions on the existence for such model with reduced-order are obtained and presented in the form of linear matrix inequalities. Finally, a numerical example is provided to demonstrate the effectiveness of the obtained results.