A novel approach for finite-frequency ℋ_∞ model reduction

This article addresses the problem of ℋ<inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</inf> model order reduction for continuous-time linear time-invariant (LTI) systems over finite-frequency intervals. The goal is to compute a reduced-order model such that the error characterised by ℋ<inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</inf>-norm between the original system and reduced-order model is minimised within a specified frequency interval. Utilising the generalised Kalman-Yakubovich-Popov lemma, the problem is formulated as an optimisation problem constrained by nonlinear matrix inequalities. By employing a novel application of the projection lemma, the problem is reformulated into an optimisation problem with linear matrix inequality constraints. An iterative algorithm is then given to compute the solution of the finite-frequency model order reduction problem. In case studies, the proposed approach is shown to outperform existing results in the literature.