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Balanced truncation of second-order systems: structure-preservation and stability

Please always quote using this URN:urn:nbn:de:0296-matheon-4109
  • We present a formal procedure for structure-preserving model reduction of linear second-order control problems. Second-order equations appear in a variety of physical contexts, e.g., vibromechanical systems or electrical circuit design to mention just a few. However typical balanced truncation methods that project onto the subspace of the largest Hankel singular values fail to preserve the problem's physical structure and may suffer from lack of stability. In this paper we adopt the framework of port-Hamiltonian systems that covers the class of relevant problems and that allows for a generalization of balanced truncation to second-order problems. We explore two possible routes to truncation of a balanced port-Hamiltonian system: one is by imposing holonomic constraints, the other one proceeds by a singular perturbation argument using an explicit scaling of the small Hankel singular values. In both cases the reduced system turns out to be port-Hamiltonian. Moreover the procedure preserves stability and passivity. For the singularly perturbed system we prove convergence of the corresponding transfer functions.

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Metadaten
Author:Carsten Hartmann, Valentina-Mira Vulcanov, Christof Schütte
URN:urn:nbn:de:0296-matheon-4109
Referee:Christof Schütte
Document Type:Preprint, Research Center Matheon
Language:English
Date of first Publication:2008/03/13
Release Date:2007/08/14
Preprint Number:480
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