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Preprint 01-2018

Linear algebra properties of dissipative Hamiltonian descriptor systems

Source file is available as :   Portable Document Format (PDF)

Author(s) : Christian Mehl , Volker Mehrmann , Michal Wojtylak

Preprint series of the Institute of Mathematics, Technische Universität Berlin
Preprint 01-2018

MSC 2000

15A18 Eigenvalues, singular values, and eigenvectors
15A21 Canonical forms, reductions, classification

Abstract :
A wide class of matrix pencils connected with dissipative Hamiltonian descriptor systems is investigated. In particular, the following properties are shown: all eigenvalues are in the closed left half plane, the nonzero finite eigenvalues on the imaginary axis are semisimple, the index is at most two, and there are restrictions for the possible left and right minimal indices. For the case that the eigenvalue zero is not semisimple, a structure-preserving method is presented that perturbs the given system into a Lyapunov stable system.

Keywords : Port Hamiltonian system, descriptor system, dissipative Hamiltonian system, matrix pencil, singular pencil, Kronecker canonical form, Lyapunov stability

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