Preprint 01-2020

Distance problems for dissipative Hamiltonian systems and related matrix polynomials

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

Preprint series of the Institute of Mathematics, Technische Universität Berlin
Preprint 01-2020

MSC 2000

15A18 Eigenvalues, singular values, and eigenvectors

15A21 Canonical forms, reductions, classification

Abstract :
We study the characterization of several distance problems for linear differential-algebraic systems with dissipative Hamiltonian structure. Since all models are only approximations of reality and data are always inaccurate, it is an important question whether a given model is close to a 'bad' model that could be considered as ill-posed or singular. This is usually done by computing a distance to the nearest model with such properties. We will discuss the distance to singularity and the distance to the nearest high index problem for dissipative Hamiltonian systems. While for general unstructured differential-algebraic systems the characterization of these distances are partially open problems, we will show that for dissipative Hamiltonian systems and related matrix polynomials there exist explicit characterizations that can be implemented numerically.

Keywords : distance to singularity, distance to high index problem, distance to instability, dissipative Hamiltonian system, differential-algebraic system, matrix pencil, Kronecker canonical form,