H∞ model reduction for singular systems: continuous-time case

The problem of H_∞ model reduction for linear singular systems in the continuous-time case is considered. The objective is to find a reduced-order system such that the associated error system is admissible and satisfies a prescribed H_∞ norm bound constraint. 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. An explicit parametrisation of all reduced-order systems is presented for the case when the related LMIs are feasible. A simple LMI condition without rank constraint is derived for the zeroth-order H_∞ approximation problem. All these results are obtained without decomposing the original system, which makes the design procedure simple and direct.