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Generalized entropy criterion for Nevanlinna-Pick interpolation with degree constraint
KTH, Superseded Departments, Mathematics.ORCID iD: 0000-0002-2681-8383
2001 (English)In: IEEE Transactions on Automatic Control, ISSN 0018-9286, E-ISSN 1558-2523, Vol. 46, no 6, 822-839 p.Article in journal (Refereed) Published
Abstract [en]

In this paper, we present a generalized entropy criterion for solving the rational Nevanlinna-Pick problem for n + 1 interpolating conditions and the degree of interpolants bounded by n, The primal problem of maximizing this entropy gain has a very well-behaved dual problem. This dual is a convex optimization problem in a finite-dimensional space and gives rise to an algorithm for finding all interpolants which are positive real and rational of degree at most n, The criterion requires a selection of a monic Schur polynomial of degree n, It follows that this class of monic polynomials completely parameterizes all such rational interpolants, and it therefore provides a set of design parameters for specifying such interpolants. The algorithm is implemented in state-space form and applied to several illustrative problems in systems and control, namely sensitivity minimization, maximal power transfer and spectral estimation.

Place, publisher, year, edition, pages
2001. Vol. 46, no 6, 822-839 p.
Keyword [en]
duality, entropy, interpolation, power transmission, robust control, spectral estimation, feedback stabilization, gain factor, uncertainty, realization, infinity, plants
URN: urn:nbn:se:kth:diva-20712ISI: 000169288100001OAI: diva2:339408
QC 20100525Available from: 2010-08-10 Created: 2010-08-10Bibliographically approved

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