Zero dynamics for networks of waves. (May 2019)

• Record Type: Journal Article
• Authors: Jacob, Birgit; Morris, Kirsten A.; Zwart, Hans
• Is Part Of: Automatica. Volume 103(2019)
• Page Start: 310
• Page End: 321
• Publication Date: 2019-05
• Subjects: Port-Hamiltonian system -- Distributed parameter systems -- Boundary control -- Zero dynamics -- Networks -- Coupled wave equations; Automatic control -- Periodicals; Automation -- Periodicals; 629.805
• DOI: 10.1016/j.automatica.2019.02.010
• Languages: English
• ISSNs: 0005-1098

Abstract

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.