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).