Combined L₂/H_∞ model reduction

Abstract

A model-reduction problem is considered which involves both L ₂ (quadratic) and H _∞ (worst-case frequency-domain) aspects. Specifically, the goal of the problem is to minimize an L ₂ model-reduction criterion subject to a prespecified H _∞ constraint on the model-reduction error. The principal result is a sufficient condition for characterizing reduced-order models with bounded L ₂ and H _∞ approximation error. The sufficient condition involves a system of modified Riccati equations coupled by an oblique projection, i.e. idempotent matrix. When the H _∞ constraint is absent, the sufficient condition specializes to the L ₂ model-reduction result given by Hyland and Bernstein (1985).