Hamiltonian Systems as Passive Systems

  • Arjan van der Schaft
Part of the Communications and Control Engineering book series (CCE)


In this chapter we deal with Euler-Lagrange and Hamiltonian systems as an important class of passive state space systems. First we consider the passivity of systems described by Euler-Lagrange equations, with an application to a tracking problem. We define the class of port-controlled Hamiltonian systems, including the examples of LC-circuits and mechanical systems with kinematic constraints. This framework is further extended to include dissipation. Stabilization procedures for port-controlled Hamiltonian systems, which exploit the Hamiltonian structure and the passivity property, are discussed. Finally, the notion of power-conserving interconnection is formalized, leading to the notion of implicit port-controlled Hamiltonian systems.


Hamiltonian System Kinematic Constraint Passive System Storage Function Dirac Structure 
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Copyright information

© Springer-Verlag London 2000

Authors and Affiliations

  • Arjan van der Schaft
    • 1
  1. 1.Faculty of Mathematical SciencesUniversity of TwenteEnschedeThe Netherlands

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