Inhalt des Dokuments
Preprint 01-2018
Linear algebra properties of dissipative Hamiltonian descriptor systems
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