Differential-algebraic systems with dissipative Hamiltonian structure

2022/08/04 by V. Mehrmann, Arjan van der Schaft, Mehrmann, V. +1 · 5 citations
Computer Science · Engineering · Mathematics · #15A18 #15A21 #15A22 #Control and Stability of Dynamical Systems #Differential Geometry (math.DG) #Dynamical Systems (math.DS) #FOS: Mathematics #Matrix Theory and Algorithms #Numerical methods for differential equations #Optimization and Control (math.OC)

paper · pdf · doi:10.48550/arxiv.2208.02737

openalex publication_date 2022/08/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Different representations of dissipative Hamiltonian and port-Hamiltonian differential-algebraic equations (DAE) systems are presented and compared. Using global geometric and algebraic points of view, translations between the 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.

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