Differential–algebraic systems with dissipative Hamiltonian structure

Volker Mehrmann; Arjan van der Schaft

doi:10.1007/s00498-023-00349-2

Differential–algebraic systems with dissipative Hamiltonian structure

Volker Mehrmann^*, Arjan van der Schaft

^*Corresponding author for this work

Bernoulli Institute

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

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Abstract

Different representations of linear dissipative Hamiltonian and port-Hamiltonian differential–algebraic equations (DAE) systems are presented and compared. Using global geometric and algebraic points of view, translations between different representations are presented. Characterizations are also derived when a general DAE system can be transformed into one of these structured representations. Approaches for computing the structural information and the described transformations are derived that can be directly implemented as numerical methods. The results are demonstrated with a large number of examples.

Original language	English
Journal	Mathematics of Control, Signals, and Systems
DOIs	https://doi.org/10.1007/s00498-023-00349-2
Publication status	E-pub ahead of print - 3-Mar-2023

Keywords

Differential–algebraic equation
Dirac structure
Dissipative Hamiltonian system
Lagrange structure
Matrix pencil
Port-Hamiltonian system

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title = "Differential–algebraic systems with dissipative Hamiltonian structure",

abstract = "Different representations of linear dissipative Hamiltonian and port-Hamiltonian differential–algebraic equations (DAE) systems are presented and compared. Using global geometric and algebraic points of view, translations between different representations are presented. Characterizations are also derived when a general DAE system can be transformed into one of these structured representations. Approaches for computing the structural information and the described transformations are derived that can be directly implemented as numerical methods. The results are demonstrated with a large number of examples.",

keywords = "Differential–algebraic equation, Dirac structure, Dissipative Hamiltonian system, Lagrange structure, Matrix pencil, Port-Hamiltonian system",

author = "Volker Mehrmann and {van der Schaft}, Arjan",

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AU - van der Schaft, Arjan

N1 - Funding Information: Open Access funding enabled and organized by Projekt DEAL. Research of the first author supported by Deutsche Forschungsgemeinschaft (DFG) through priority Program SPP 1984 within project 790 39-2: Distributed dynamic control of network security. Publisher Copyright: © 2023, The Author(s).

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N2 - Different representations of linear dissipative Hamiltonian and port-Hamiltonian differential–algebraic equations (DAE) systems are presented and compared. Using global geometric and algebraic points of view, translations between different representations are presented. Characterizations are also derived when a general DAE system can be transformed into one of these structured representations. Approaches for computing the structural information and the described transformations are derived that can be directly implemented as numerical methods. The results are demonstrated with a large number of examples.

AB - Different representations of linear dissipative Hamiltonian and port-Hamiltonian differential–algebraic equations (DAE) systems are presented and compared. Using global geometric and algebraic points of view, translations between different representations are presented. Characterizations are also derived when a general DAE system can be transformed into one of these structured representations. Approaches for computing the structural information and the described transformations are derived that can be directly implemented as numerical methods. The results are demonstrated with a large number of examples.

KW - Differential–algebraic equation

KW - Dirac structure

KW - Dissipative Hamiltonian system

KW - Lagrange structure

KW - Matrix pencil

KW - Port-Hamiltonian system

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JO - Mathematics of Control, Signals, and Systems (MCSS)

JF - Mathematics of Control, Signals, and Systems (MCSS)

ER -

Differential–algebraic systems with dissipative Hamiltonian structure

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Keywords

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