An LMI approach to H∞ model reduction of linear discrete-time systems over finite frequency interval

In this paper, we address the finite-frequency H_∞ model reduction problem for linear time-invariant discrete-time systems. Different from the existing methods in the literature, we resort to the aid of recently developed Generalized Kalman-Yakubovich-Popov (GKYP) lemma. Based on in-depth exploitation of GKYP lemma and Projection lemma, sufficient conditions for the finite frequency H_∞ model reduction problems are derived and expressed in terms of solutions to a set of linear matrix inequalities (LMIs) which can be handled easily by using the available toolbox. These results can be regarded as complete counterparts of those recently obtained in the continuous-time system setting.