H ∞ deconvolution filtering of 2-D digital systems

This paper deals with the problem of two-dimensional (2-D) digital system deconvolution under the H-infinity performance specification. The 2-D digital system under consideration is expressed by the Fornasini–Marchesini local state-space (FM LSS) model. For a given 2-D digital system, a 2-D deconvolution filter is designed to reconstruct the 2-D signal to meet a prescribed H-infinity performance specification. A key analytical means for the deconvolution filter design is the 2-D bounded realness property derived in this paper. Applying this property, the 2-D H-infinity deconvolution filter design is formulated into a convex optimization problem characterized by linear matrix inequalities (LMIs). A procedure for the design of an H-infinity deconvolution filter for a given 2-D digital system with measurement noise is developed first. The LMI approach to the 2-D H-infinity deconvolution filtering problem is further extended to the H-infinity 2-D robust deconvolution filtering problem with polytopic modeling uncertainties in the 2-D system. The obtained results on the 2-D deconvolution filtering and robust deconvolution filtering problems are demonstrated with examples.