Authors

Arjan van der Schaft

Abstract

As described in the previous Chaps.  3 and 4 , (cyclo-)passive systems are defined by the existence of a storage function (nonnegative in case of passivity) satisfying the dissipation inequality with respect to the supply rate \( \)s(u,y)=u^Ty\( \) s ( u , y ) = u T y . In contrast, port-Hamiltonian systems, the topic of the current chapter are endowed with the property of (cyclo-)passivity as a consequence of their system formulation. In fact, port-Hamiltonian systems arise from first principles physical modeling. They are defined in terms of a Hamiltonian function together with two geometric structures (corresponding, respectively, to power-conserving interconnection and energy dissipation), which are such that the Hamiltonian function automatically satisfies the dissipation inequality.

Citation

BibTeX

@inbook{van_der_Schaft_2016,
  title={{Port-Hamiltonian Systems}},
  ISBN={9783319499925},
  ISSN={2197-7119},
  DOI={10.1007/978-3-319-49992-5_6},
  booktitle={{L2-Gain and Passivity Techniques in Nonlinear Control}},
  publisher={Springer International Publishing},
  author={van der Schaft, Arjan},
  year={2016},
  pages={113--171}
}

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