Km. Grigoriadis et Jt. Watson, REDUCED-ORDER H-INFINITY AND L-2-L-INFINITY FILTERING VIA LINEAR MATRIX INEQUALITIES, IEEE transactions on aerospace and electronic systems, 33(4), 1997, pp. 1326-1338
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.