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

This paper is concerned with the H∞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∞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.