H∞ model reduction for T‐S fuzzy systems over finite frequency ranges

Summary This paper investigates the H∞ model reduction problem over finite frequency ranges for continuous time Takagi‐Sugeno (T‐S) fuzzy systems. Given an asymptotically stable system, our aim is to find a stable reduced‐order system in such a way that the error of the transfer function between the original system and the reduced‐order one is bounded over a finite frequency range. By using the Finsler's lemma, new sufficient conditions in terms of linear matrix inequalities are derived in different frequency ranges. These conditions provide extra degrees of freedom in the optimization of the H∞ performance when the frequency range of noises is known beforehand. Finally, we demonstrate via numerical examples that our method can achieve much smaller approximation error than existing approaches.