$\mathscr{H}_{\infty}$ filter design with low- and middle-frequency specifications for continuous-time linear systems: LMI conditions derived from two different extensions of the KYP lemma

This paper addresses the full-order filtering problem with low- and middle-frequency \mathscrH∞ specifications for continuous-time linear systems. Two distinct extensions of the KYP Lemma are used to produce synthesis conditions capable to cope with the frequency specifications. A comparison between the results obtained with the two extensions in terms of numerical complexity and the bound provided for the \mathscrH∞ norm is made by means of numerical examples. The design conditions, given in the form of linear matrix inequalities, can also cope with polytopic time-invariant linear systems. Two main contributions distinguish this paper from previous results: i) a simpler condition to assure asymptotic stability of the filtered system; ii) a new synthesis condition based on an alternative extension of the KYP Lemma.