Reduced-order H∞ and L2-L∞ 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_∞ and L₂-L_∞ filtering problems. These conditions are expressed in terms of linear matrix inequalities (LMIs) and a coupling nonconvex matrix rank constraint. Convex LMI problems are obtained for the full-order and the zeroth-order filtering. An explicit parametrization of all reduced-order filters 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.