Zero dynamics for networks of waves

Birgit Jacob* (Corresponding Author), Kirsten A. Morris, Hans Zwart

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review

1 Citation (Scopus)
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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.

Original languageEnglish
Pages (from-to)310-321
Number of pages12
Early online date23 Feb 2019
Publication statusPublished - 1 May 2019


  • Boundary control
  • Coupled wave equations
  • Distributed parameter systems
  • Networks
  • Port-Hamiltonian system
  • Zero dynamics


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