L-2 and L-2-L-infinity model reduction via linear matrix inequalities

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