OPTIMAL H-INFINITY MODEL-REDUCTION VIA LINEAR MATRIX INEQUALITIES - CONTINUOUS-TIME AND DISCRETE-TIME CASES

Necessary and sufficient conditions are derived for the existence of a solution to the continuous-time and discrete-time H-infinity model re duction problems. These conditions are expressed in terms of linear ma trix inequalities (LMIs) and a coupling non-convex rank constraint set . In addition, an explicit parametrization of all reduced-order models that correspond to a feasible solution is provided in terms of a cont ractive matrix. These results follow from the recent solution of the H -infinity control design problem using LMIs. Particularly simple condi tions and a simple parametrization of all solutions are obtained for t he zeroth-order H-infinity approximation problem, and the convexity of this problem is demonstrated. Computational issues are discussed and an iterative procedure is proposed to solve the H-infinity model reduc tion problem using alternating projections, although global convergenc e of the algorithm is not guaranteed.