Port-Hamiltonian Realizations of Positive Real Descriptor Systems
Optimization and Control
2024-08-27 v1 Numerical Analysis
Numerical Analysis
Abstract
The relationship between port-Hamiltonian and positive real descriptor systems is investigated. It is well-known that port-Hamiltonian systems are positive real, but the converse implication does not always hold. In [K. Cherifi, H. Gernandt, and D. Hinsen. The difference between port-Hamiltonian, passive and positive real descriptor systems. Math. Control Signals Systems, pages 1-32, 2023] sufficient conditions for the converse are presented. We refine these conditions and present for a completely controllable, completely observable and positive real descriptor system a necessary and sufficient condition as well as an explicit method to compute a port-Hamiltonian realization of a general positive real descriptor system.
Keywords
Cite
@article{arxiv.2408.14115,
title = {Port-Hamiltonian Realizations of Positive Real Descriptor Systems},
author = {Delin Chu and Volker Mehrmann},
journal= {arXiv preprint arXiv:2408.14115},
year = {2024}
}