L/sub 2/ and L/sub 2/-L/sub /spl infin// model reduction via linear matrix inequalities

Necessary and sufficient conditions are derived for the existence of a solution to the continuous-time and discrete-time suboptimal L/sub 2/ and L/sub 2/-L/sub /spl infin// model reduction problems. These conditions are expressed in terms of linear matrix inequalities (LMIs) and a coupling non-convex rank constraint set. In addition, explicit parametrizations of all reduced-order models that correspond to a feasible solution are presented in terms of contractive matrices.