Zero dynamics for networks of waves

Birgit Jacob; Kirsten A. Morris; Hans Zwart

doi:10.1016/j.automatica.2019.02.010

Zero dynamics for networks of waves

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

^*Corresponding author for this work

Hybrid Systems

Research output: Contribution to journal › Article › Academic › peer-review

7 Citations (Scopus)

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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 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 language	English
Pages (from-to)	310-321
Number of pages	12
Journal	Automatica
Volume	103
Early online date	23 Feb 2019
DOIs	https://doi.org/10.1016/j.automatica.2019.02.010
Publication status	Published - 1 May 2019

Keywords

2019 OA procedure
Coupled wave equations
Distributed parameter systems
Networks
Port-Hamiltonian system
Zero dynamics
Boundary control

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10.1016/j.automatica.2019.02.010

Automatica-JacobMorrisZwart-finalAccepted author version, 409 KBLicence: CC BY-NC-ND
zeroFinal published version, 628 KBLicence: Taverne

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title = "Zero dynamics for networks of waves",

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.",

keywords = "2019 OA procedure, Coupled wave equations, Distributed parameter systems, Networks, Port-Hamiltonian system, Zero dynamics, Boundary control",

author = "Birgit Jacob and Morris, \{Kirsten A.\} and Hans Zwart",

year = "2019",

month = may,

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doi = "10.1016/j.automatica.2019.02.010",

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volume = "103",

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journal = "Automatica",

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T1 - Zero dynamics for networks of waves

AU - Jacob, Birgit

AU - Morris, Kirsten A.

AU - Zwart, Hans

PY - 2019/5/1

Y1 - 2019/5/1

N2 - 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.

AB - 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.

KW - 2019 OA procedure

KW - Coupled wave equations

KW - Distributed parameter systems

KW - Networks

KW - Port-Hamiltonian system

KW - Zero dynamics

KW - Boundary control

UR - https://www.scopus.com/pages/publications/85061900695

U2 - 10.1016/j.automatica.2019.02.010

DO - 10.1016/j.automatica.2019.02.010

M3 - Article

AN - SCOPUS:85061900695

SN - 0005-1098

VL - 103

SP - 310

EP - 321

JO - Automatica

JF - Automatica

ER -

Zero dynamics for networks of waves

Abstract

Keywords

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