Km. Grigoriadis, OPTIMAL H-INFINITY MODEL-REDUCTION VIA LINEAR MATRIX INEQUALITIES - CONTINUOUS-TIME AND DISCRETE-TIME CASES, Systems & control letters, 26(5), 1995, pp. 321-333
Citations number
36
Categorie Soggetti
Controlo Theory & Cybernetics","System Science","Operatione Research & Management Science
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.