Zero dynamics for networks of waves
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Jacob, Birgit
Morris, Kirsten
Zwart, Hans
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Elsevier
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 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 a well-posed system, 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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The final publication is available at Elsevier via https://doi.org/10.1016/j.automatica.2019.02.010. © 2019. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/
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Except where otherwise noted, this item's license is described as Attribution-NonCommercial-NoDerivatives 4.0 International