Combined H2/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 in Hyland and Bernstein, 1985. The full version of this paper can be found in Haddad and Bernstein, 1989.