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Preprint 06-2017

Port-Hamiltonian descriptor systems

Source file is available as :   Portable Document Format (PDF)

Author(s) : Christopher Beattie , Volker Mehrmann , Hongguo Xu , Hans Zwart

Preprint series of the Institute of Mathematics, Technische Universität Berlin
Preprint 06-2017

MSC 2000

93A30 Mathematical modeling
93B11 System structure simplification

Abstract :
The modeling framework of port-Hamiltonian systems is systematically extended to constrained dynamical systems (descriptor systems, differential-algebraic equations). A new algebraically and geometrically defined system structure is derived. It is shown that this structure is invariant under equivalence transformations, and that it is adequate also for the modeling of high-index descriptor systems. The regularization procedure for descriptor systems to make them suitable for simulation and control is modified to deal with the port-Hamiltonian structure. The relevance of the new structure is demonstrated with several examples.

Keywords : port-Hamiltonian system, descriptor system, differential-algebraic equation, passivity, stability, system transformation, differentiation-index, strangeness-index, skew-adjoint operator

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