Differential–algebraic systems with dissipative Hamiltonian structure

Volker Mehrmann*, Arjan van der Schaft

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review

6 Citations (Scopus)
22 Downloads (Pure)


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 languageEnglish
Pages (from-to)541-584
Number of pages44
JournalMathematics of Control, Signals, and Systems
Early online date3-Mar-2023
Publication statusPublished - Sept-2023


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


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