Port-Hamiltonian Differential-Algebraic Systems

  • A. J. van der SchaftEmail author
Part of the Differential-Algebraic Equations Forum book series (DAEF)


The basic starting point of port-Hamiltonian systems theory is network modeling; considering the overall physical system as the interconnection of simple subsystems, mutually influencing each other via energy flow. As a result of the interconnections algebraic constraints between the state variables commonly arise. This leads to the description of the system by differential-algebraic equations (DAEs), i.e., a combination of ordinary differential equations with algebraic constraints. The basic point of view put forward in this survey paper is that the differential-algebraic equations that arise are not just arbitrary, but are endowed with a special mathematical structure; in particular with an underlying geometric structure known as a Dirac structure. It will be discussed how this knowledge can be exploited for analysis and control.


Port-Hamiltonian systems Passivity Algebraic constraints Kinematic constraints Casimirs Switching systems Dirac structure Interconnection 

Mathematics Subject Classification (2010)

34A09 37J05 70G45 93B10 93B27 93C10 



This survey article is based on joint work with many colleagues, whom I thank for a very stimulating collaboration. In particular I thank Bernhard Maschke for continuing joint efforts over the years.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.Johann Bernoulli Institute for Mathematics and Computer ScienceUniversity of GroningenGroningenThe Netherlands

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