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Checking dissipativity of behavioral systems using para-Hermitian matrix polynomials

Please always quote using this URN:urn:nbn:de:0296-matheon-6789
  • The behavior approach and the problem of dissipativity have both been introduced and studied extensively by Willems et al. However, a computationally feasible method to check dissipativity is missing. Current methods will mostly rely on symbolic representations of rational functions. We will discuss a new characterization for linear systems in behavior form that allows to check dissipativity via the solution of a para-Hermitian, polynomial eigenvalue problem. Thus, we can employ standard methods of cubic complexity.

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Metadaten
Author:Tobias Brüll
URN:urn:nbn:de:0296-matheon-6789
Referee:Volker Mehrmann
Document Type:Preprint, Research Center Matheon
Language:English
Date of first Publication:2010/01/22
Release Date:2010/01/22
Tag:
Institute:Technische Universität Berlin
MSC-Classification:15-XX LINEAR AND MULTILINEAR ALGEBRA; MATRIX THEORY / 15Bxx Special matrices / 15B57 Hermitian, skew-Hermitian, and related matrices
34-XX ORDINARY DIFFERENTIAL EQUATIONS / 34Axx General theory / 34A09 Implicit equations, differential-algebraic equations [See also 65L80]
47-XX OPERATOR THEORY / 47Hxx Nonlinear operators and their properties (For global and geometric aspects, see 58-XX, especially 58Cxx) / 47H60 Multilinear and polynomial operators [See also 46G25]
93-XX SYSTEMS THEORY; CONTROL (For optimal control, see 49-XX) / 93-02 Research exposition (monographs, survey articles)
Preprint Number:683
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