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Matrix-valued Nevanlinna-pick interpolation with complexity constraint: An optimization approach
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.ORCID iD: 0000-0002-2681-8383
2003 (English)In: IEEE Transactions on Automatic Control, ISSN 0018-9286, E-ISSN 1558-2523, Vol. 48, no 12, 2172-2190 p.Article in journal (Refereed) Published
Abstract [en]

Over the last several years, a new theory of Nevanlinna-Pick interpolation with complexity constraint has been developed for scalar interpolants. In this paper we generalize this theory to the matrix-valued, case, also allowing for multiple interpolation points. We parameterize a class of interpolants consisting of "most interpotants" of no higher degree than the central solution in terms of spectral zeros. This is a complete parameterization, and for each choice of interpolant we provide a convex optimization problem for determining it. This is derived in the context of duality theory of mathematical programming. To solve the convex optimization problem, we employ a homotopy continuation technique previously developed for the scalar case. These results can be applied to many classes of engineering problems,and, to illustrate this, we provide some,examples. In particular, we apply our method to a benchmark problem in multivariate robust control. By constructing a controller satisfying all design specifications but having only half the McMillan degree of conventional H-infinity controllers, we demonstrate the advantage of the proposed method.

Place, publisher, year, edition, pages
2003. Vol. 48, no 12, 2172-2190 p.
Keyword [en]
complexity constraint, H-infinity control, matrix-valued, Nevanlinna-Pick interpolation, optimization, spectral estimation, h-infinity control, feedback stabilization, gain factor, systems, uncertainty, reduction, plants
National Category
Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-23047DOI: 10.1109/tac.2003.820227ISI: 000187577300009OAI: oai:DiVA.org:kth-23047DiVA: diva2:341745
Note
QC 20100525 NR 20140804Available from: 2010-08-10 Created: 2010-08-10 Last updated: 2017-12-12Bibliographically approved

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Lindquist, Anders

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