Stability radii for real linear Hamiltonian systems with perturbed dissipation
Please always quote using this URN:urn:nbn:de:0296-matheon-13926
- We study linear dissipative Hamiltonian (DH) systems with real constant coefficients that arise in energy based modeling of dynamical systems. In this paper we analyze when such a system is on the boundary of the region of asymptotic stability, i.e., when it has purely imaginary eigenvalues, or how much the dissipation term has to be perturbed to be on this boundary. For unstructured systems the explicit construction of the \emph{real distance to instability (real stability radius)} has been a challenging problem. In this paper, we analyze this real distance under different structured perturbations to the dissipation term that preserve the DH structure and we derive explicit formulas for this distance in terms of low rank perturbations. We also show (via numerical examples) that under real structured perturbations to the dissipation the asymptotical stability of a DH system is much more robust than for unstructured perturbations.
Author: | Christian Mehl, Volker Mehrmann, Punit Sharma |
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URN: | urn:nbn:de:0296-matheon-13926 |
Referee: | Caren Tischendorf |
Document Type: | Preprint, Research Center Matheon |
Language: | English |
Date of first Publication: | 2016/09/01 |
Release Date: | 2016/09/01 |
Tag: | dissipative Hamiltonian system; port-Hamiltonian system; real distance to instability; real structured distance to instability; restricted real distance to instability |
Institute: | Research Center Matheon |
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: | 1110 |