H∞ reduced-order approximation of 2-D digital filters

This paper considers the H-infinity reduced-order approximation of two-dimensional (2-D) digital filters using the linear matrix inequality (LMI) approach. The 2-D digital filter is described by the 2-D Roesser model. We shall first establish LMI conditions for which a 2-D system is bounded real. This bounded realness property then allows us to derive solvability conditions for the 2-D H-infinity reduced-order approximation which in general involves a nonconvex matrix rank minimization subject to LMI constraints. A numerical procedure is proposed to obtain a reduced-order H-infinity approximation of the given 2-D filter using alternating projections, In particular, when a zeroth-order 2-D H-infinity approximation is desired, it is shown that the approximation problem boils down to a convex LMI optimization problem. Numerical examples are given to demonstrate the proposed 2-D H-infinity reduced-order approximation approach.