Port-Hamiltonian Realizations of Linear Time Invariant Systems

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Author(s) : Christopher Beattie , Volker Mehrmann , Hongguo Xu

Preprint series of the Institute of Mathematics, Technische Universität Berlin
Preprint 23-2015

MSC 2000

93A30 Mathematical modeling
93B17 Transformations

Abstract :
The question when a general linear time invariant control system is equivalent to a port-Hamiltonian systems is answered. Several equivalent characterizations are derived which extend the characterizations of Willems to the general non-minimal case. An explicit construction of the transformation matrices is presented. The methods are applied in the stability analysis of disc brake squeal.

Keywords : port-Hamiltonian system, passivity, stability, system transformation, linear matrix inequality, Lyapunov inequality, even pencil, quadratic eigenvalue problem