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Structured distances to instability for linear Hamiltonian systems with dissipation

Please always quote using this URN:urn:nbn:de:0296-matheon-13770
  • Dissipative Hamiltonian (DH) systems are an important concept in energy based modeling of dynamical systems. One of the major advantages of the DH formulation is that the system encodes system properties in an algebraic way in the system. Making use of the structure, it is easy to see that DH systems are stable. In this paper the question is discussed when a linear constant coefficient DH system is on the boundary of the region of asymptotic stability, i.e., when it has purely imaginary eigenvalues, or how much it has to be perturbed to be on this boundary. For unstructured systems this distance to instability (stability radius) is well-understood. In this paper, explicit formulas for this distance under structure preserving perturbations are determined. It is also shown (via numerical examples) that under structured perturbations the asymptotical stability of a DH system is much more robust than for unstructured perturbations, since the distance can be much larger.

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Metadaten
Author:Christian Mehl, Volker Mehrmann, Punit Sharma
URN:urn:nbn:de:0296-matheon-13770
Referee:Caren Tischendorf
Document Type:Preprint, Research Center Matheon
Language:English
Date of first Publication:2016/04/01
Release Date:2016/04/01
Tag:dissipative Hamiltonian system; distance to instability; port-Hamiltonian system; restricted distance to instability; structrured distance to instability
Institute:Technische Universität Berlin
Project:C Energy and Materials (Production) / C-SE3 Stability analysis of power networks and power network models
MSC-Classification:65-XX NUMERICAL ANALYSIS / 65Fxx Numerical linear algebra / 65F15 Eigenvalues, eigenvectors
93-XX SYSTEMS THEORY; CONTROL (For optimal control, see 49-XX) / 93Dxx Stability / 93D09 Robust stability
93-XX SYSTEMS THEORY; CONTROL (For optimal control, see 49-XX) / 93Dxx Stability / 93D20 Asymptotic stability
Preprint Number:1107
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