H_∞ model reduction of 2D discrete-time T-S fuzzy systems

This paper considers the problem of H_∞ model reduction design for two-dimensional (2D) discrete-time Takagi-Sugeno (T-S) fuzzy systems described by Roesser model, over finite frequency (FF) domain. The problem to be solved in the paper is to find a reduced-order model such that the approximation error system is asymptotically stable, which is able to approximate the original T-S fuzzy system with comparatively small and minimised H_∞ performance when frequency ranges of noises are known beforehand. Via the use of the generalised Kalman Yakubovich Popov (gKYP) lemma, new design conditions guaranteeing the FF H_∞ model reduction are established in terms of linear matrix inequalities (LMIs). To highlight the effectiveness of the proposed H_∞ model reduction design, a numerical example is given to illustrate the effectiveness and the less conservativeness of the proposed approach.