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-inf inity and L-2 - L-infinity filtering problems. These conditions are ex pressed in terms of linear matrix inequalities (LMIs) and a coupling n onconvex matrix rank constaint. Convex LMI problems are obtained for t he full-order and the zeroth-order filtering. An explicit parametrizat ion of all reduced-order tilters that correspond to a feasible solutio n is derived in terms of a contractive matrix, and iterative algorithm s are proposed to solve the reduced-order filtering problems using alt ernating projections.