TY - GEN A1 - Mehl, Christian A1 - Mehrmann, Volker A1 - Sharma, Punit T1 - Structured distances to instability for linear Hamiltonian systems with dissipation N2 - 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. KW - dissipative Hamiltonian system KW - port-Hamiltonian system KW - distance to instability KW - structrured distance to instability KW - restricted distance to instability Y1 - 2016 UR - https://opus4.kobv.de/opus4-matheon/frontdoor/index/index/docId/1377 UR - https://nbn-resolving.org/urn:nbn:de:0296-matheon-13770 ER -