H∞ model reduction for discrete-time singular systems

Abstract

This paper investigates the problem of H∞ model reduction for linear discrete-time singular systems. Without decomposing the original system matrices, necessary and sufficient conditions for the solvability of this problem are obtained in terms of linear matrix inequalities (LMIs) and a coupling non-convex rank constraint set. When these conditions are feasible, an explicit parametrization of the desired reduced-order models is given. Particularly, a simple LMI condition without rank constraint is derived for the zeroth-order H∞ approximation problem. Finally, an illustrative example is provided to demonstrate the applicability of the proposed approach. © 2002 Elsevier Science B.V. All rights reserved.