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arXiv · 1711.07020

Zero Dynamics for Port-Hamiltonian Systems

Birgit Jacob·Kirsten A. Morris·Hans Zwart
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Abstract

The zero dynamics of infinite-dimensional systems can be difficult to characterize. The zero dynamics of boundary control systems are particularly problematic. In this paper the zero dynamics of port-Hamiltonian systems are studied. A complete characterization of the zero dynamics for a port-Hamiltonian systems with invertible feedthrough as another port-Hamiltonian system on the same state space is given. It is shown that the zero dynamics for any port-Hamiltonian system with commensurate wave speeds are well-defined, and are also a port-Hamiltonian system. Examples include wave equations with uniform wave speed on a network. A constructive procedure for calculation of the zero dynamics, that can be used for very large system order, is provided.

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Birgit Jacob, Kirsten A. Morris, Hans Zwart. 2017-11-19. Zero Dynamics for Port-Hamiltonian Systems. https://arxiv.org/abs/1711.07020

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