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BIT Numerical Mathematics

, Volume 57, Issue 3, pp 811–843 | Cite as

Stability radii for real linear Hamiltonian systems with perturbed dissipation

  • Christian Mehl
  • Volker MehrmannEmail author
  • Punit Sharma
Article

Abstract

We study linear dissipative Hamiltonian (DH) systems with real constant coefficients that arise in energy based modeling of dynamical systems. 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 real distance to instability (real stability radius) has been a challenging problem. 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.

Keywords

Dissipative Hamiltonian system Port-Hamiltonian system Real distance to instability Real structured distance to instability Restricted real distance to instability 

Mathematics Subject Classification

93D20 93D09 65F15 15A21 65L80 65L05 34A30 

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Copyright information

© Springer Science+Business Media Dordrecht 2017

Authors and Affiliations

  1. 1.Institut für MathematikTechnische Universität BerlinBerlinGermany

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