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A class of damping models preserving eigenspaces for linear conservative port-Hamiltonian systems

Matignon, Denis and Hélie, Thomas A class of damping models preserving eigenspaces for linear conservative port-Hamiltonian systems. (2013) European Journal of control, 19 (6). 486-494. ISSN 0947-3580

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Official URL: http://dx.doi.org/10.1016/j.ejcon.2013.10.003

Abstract

For conservative mechanical systems, the so-called Caughey series are known to define the class of damping matrices that preserve eigenspaces. In particular, for finite-dimensional systems, these matrices prove to be a polynomial of one reduced matrix, which depends on the mass and stiffness matrices. Damping is ensured whatever the eigenvalues of the conservative problem if and only if the polynomial is positive for positive scalar values. This paper first recasts this result in the port-Hamiltonian framework by introducing a port variable corresponding to internal energy dissipation (resistive element). Moreover, this formalism naturally allows to cope with systems including gyroscopic effects (gyrators). Second, generalizations to the infinite-dimensional case are considered. They consists of extending the previous polynomial class to rational functions and more general functions of operators (instead of matrices), once the appropriate functional framework has been defined. In this case, the resistive element is modelled by a given static operator, such as an elliptic PDE. These results are illustrated on several PDE examples: the Webster horn equation, the Bernoulli beam equation; the damping models under consideration are fluid, structural, rational and generalized fractional Laplacian or bi-Laplacian.

Item Type:Article
Additional Information:Thanks to Elsevier editor. The definitive version is available at http://www.sciencedirect.com The original PDF of the article can be found at European Journal of control website: http://www.sciencedirect.com/science/journal/09473580/19/6
Audience (journal):International peer-reviewed journal
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Institution:Université de Toulouse > Institut Supérieur de l'Aéronautique et de l'Espace - ISAE-SUPAERO (FRANCE)
Other partners > Institut de Recherche et Coordination Acoustique/Musique - IRCAM (FRANCE)
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Deposited By: Denis Matignon
Deposited On:25 Apr 2013 09:43

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