Combined L2/H∞model reduction

A model-reduction problem is considered which involves both L2 (quadratic) and H∞ (worst-case frequency-domain) aspects. Specifically, the goal of the problem is to minimize an L2 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 L2 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 L2 model-reduction result given by Hyland and Bernstein (1985).