Construction of discrete-time models for port-controlled Hamiltonian systems with applications

Dina Shona Laila, A. Astolfi

Research output: Contribution to journalArticle

22 Citations (Scopus)

Abstract

The issues of constructing a discrete-time model for Hamiltonian systems are in general different from those for dissipative systems. We propose an algorithm for constructing an approximate discrete-time model, which guarantees Hamiltonian conservation. We show that the algorithm also preserves, in a weaker sense, the losslessness property of a class of port-controlled Hamiltonian systems. An application of the algorithm to port-controlled Hamiltonian systems with quadratic Hamiltonian is presented, and we use this to solve the stabilization problem for this class of systems based on the approximate discrete-time model constructed using the proposed algorithm. We illustrate the usefulness of the algorithm in designing a discrete-time controller to stabilize the angular velocity of the dynamics of a rigid body.
Original languageEnglish
Pages (from-to)673-680
JournalSystems & Control Letters
Volume55
Issue number8
DOIs
Publication statusPublished - 25 Apr 2006

Bibliographical note

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Keywords

  • Hamiltonian systems
  • Discrete-time systems
  • Hamiltonian conservation
  • Stabilization
  • Nonlinear systems

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