H _∞ model reduction of 2-D dingular roesser models

This paper discusses the problem of H _∞ model reduction for linear discrete time 2-D singular Roesser models (2-D SRM). A condition for bounded realness is established for 2-D SRM in terms of linear matrix inequalities (LMIs). Based on this, a sufficient condition for the solvability of the H _∞ model reduction problem is obtained via a group of LMIs and a set of coupling non-convex rank constraints. An explicit parameterization of the desired reduced-order models is presented. Particularly, a simple LMI condition without rank constraints is proposed for the zeroth-order H _∞ approximation problem. Finally, a numerical example is given to illustrate the applicability of the proposed approach.