Linear port-Hamiltonian DAE systems revisited

2022/11/12 by Arjan van der Schaft, Volker Mehrmann, van der Schaft, Arjan +1 · 3 citations
Computer Science · Engineering · Mathematics · #34A09 #37J06 #93C05 #Control and Stability of Dynamical Systems #FOS: Mathematics #Modeling and Simulation Systems #Numerical Analysis (math.NA) #Numerical methods for differential equations #Optimization and Control (math.OC)

paper · pdf · doi:10.48550/arxiv.2211.06676

openalex publication_date 2022/11/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Port-Hamiltonian systems theory provides a systematic methodology for the modeling, simulation and control of multi-physics systems. The incorporation of algebraic constraints has led to a multitude of definitions of port-Hamiltonian differential-algebraic equations (DAE) systems. This paper presents extensions of results in Gernandt, Haller & Reis (2021) and Mehrmann & Van der Schaft (2022) in the context of maximally monotone structures and shows that any such space can be written as composition of a Dirac and a resistive structure. Furthermore, appropriate coordinate representations are presented as well as explicit expressions for the associated transfer functions.

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• Output feedback stabilization of linear port-Hamiltonian descriptor systems
• Canonical forms for pairs of matrices associated with Lagrangian and Dirac subspaces
• Weak solutions of port-Hamiltonian systems

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