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 expresse
d in terms of linear matrix inequalities (LMIs) and a coupling non-con
vex rank constraint. In addition, explicit parametrizations of all red
uced-order models that correspond to a feasible solution are presented
in terms of contractive matrices.