Infinite-dimensional port-Hamiltonian systems: a system node approach

We consider an operator-theoretic approach to linear infinite-dimensional port-Hamiltonian systems. In particular, we use the theory of system nodes as reported by Staffans (Well-posed linear systems. Encyclopedia of mathematics and its applications, Cambridge University Press, Cambridge, UK, 2005)...

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Bibliographic Details
Published in:Mathematics of control, signals, and systems Vol. 37; no. 3; pp. 573 - 620
Main Authors: Philipp, Friedrich M., Reis, Timo, Schaller, Manuel
Format: Journal Article
Language:English
Published: London Springer London 01.09.2025
Springer Nature B.V
Subjects:
Communications Engineering
Control
Energy
Hamiltonian functions
Hilbert space
Hyperbolic systems
Linear systems
Mathematics
Mathematics and Statistics
Mechatronics
Networks
Ordinary differential equations
Original Article
Partial differential equations
Robotics
System theory
Systems Theory
Boundary control
Infinite-dimensional systems
System nodes
Port-Hamiltonian systems
ISSN:0932-4194, 1435-568X
Online Access:Get full text
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Summary:We consider an operator-theoretic approach to linear infinite-dimensional port-Hamiltonian systems. In particular, we use the theory of system nodes as reported by Staffans (Well-posed linear systems. Encyclopedia of mathematics and its applications, Cambridge University Press, Cambridge, UK, 2005) to formulate a suitable concept for port-Hamiltonian systems, which allows a unifying approach to systems with boundary as well as distributed control and observation. The concept presented in this article is further neither limited to parabolic nor hyperbolic systems, and it also covers partial differential equations on multi-dimensional spatial domains. Our presented theory is substantiated by means of several physical examples.
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ISSN:0932-4194
1435-568X
DOI:10.1007/s00498-025-00412-0