Polytopic energy-to-peak filter design for uncertain continuous systems over finite frequency ranges

A new approach for the synthesis of polytopic $ L_{2}-L_{\infty } $ L2−L∞ filters is proposed for uncertain systems over Finite Frequency (FF) ranges. The novelty derives from the use of FF specifications combined with the $ L_{2}-L_{\infty } $ L2−L∞ performance index: First, conditions are provided for the asymptotic stability of the polytopic augmented systems, by trace calculation of matrices and the use of Finsler's Lemma. Then, synthesis conditions are proposed as LMIs for the polytopic filter parameters over several FF intervals. Furthermore, the use of slack matrices through Finsler's Lemma provides design conditions with less conservative outcomes. A numerical example is solved and simulated to demonstrate the effectiveness of the ongoing approach when compared with previous results in the literature.