Finite-frequency model reduction of discrete-time T–S fuzzy state-delay systems

This paper is concerned with the problem of model reduction for discrete-time Takagi–Sugeno (T–S) fuzzy state-delay systems with finite-frequency input signals. A new finite-frequency model reduction algorithm is proposed, which can get a better approximation performance than the existing full-frequency methods. Firstly, a finite-frequency H∞H∞ performance index is defined in the frequency domain. Then, a stability condition and a finite-frequency H∞H∞ performance analysis condition are developed by the aid of Jensen׳s inequality and Parseval׳s theorem, respectively. Based on these conditions, sufficient model reduction conditions are derived for discrete-time T–S fuzzy state-delay systems. An optimization algorithm is proposed to obtain a stable reduced-order model satisfying the finite-frequency performance specification. Finally, the effectiveness of the proposed method is illustrated by a numerical example.