Reduced-order H-infinity and L-2-L-infinity filtering via linear matrix inequalities

Necessary and sufficient conditions are derived for the existence of a solution to the continuous-time and discrete-time reduced-order H-infinity and L-2 - L-infinity filtering problems. These conditions are expressed in terms of linear matrix inequalities (LMIs) and a coupling nonconvex matrix rank constaint. Convex LMI problems are obtained for the full-order and the zeroth-order filtering. An explicit parametrization of all reduced-order tilters that correspond to a feasible solution is derived in terms of a contractive matrix, and iterative algorithms are proposed to solve the reduced-order filtering problems using alternating projections.