An LMI approach to stabilization of linear port-controlled Hamiltonian systems

Authors

Stephen Prajna, Arjan van der Schaft, Gjerrit Meinsma

Abstract

In this paper, it is shown that controllers for stabilizing linear port-controlled Hamiltonian (PCH) systems via interconnection and damping assignment can be obtained by solving a set of linear matrix inequalities (LMIs). Two sets of (almost) equivalent LMIs are proposed. In the first set, the interconnection and damping matrices do not appear explicitly, which makes it more difficult to directly manipulate those matrices. By requiring the system to have no uncontrollable pole at s=0, the second set of LMIs, explicitly containing the interconnection and damping matrices, can be obtained. Taking into account the physical properties of the system, some prespecified structures can be imposed directly on those matrices.

Keywords

Stabilization; Interconnection assignment; Damping; Hamiltonian systems

Citation

Journal: Systems & Control Letters
Year: 2002
Volume: 45
Issue: 5
Pages: 371–385
Publisher: Elsevier BV
DOI: 10.1016/s0167-6911(01)00195-5

BibTeX

@article{Prajna_2002,
  title={{An LMI approach to stabilization of linear port-controlled Hamiltonian systems}},
  volume={45},
  ISSN={0167-6911},
  DOI={10.1016/s0167-6911(01)00195-5},
  number={5},
  journal={Systems &amp; Control Letters},
  publisher={Elsevier BV},
  author={Prajna, Stephen and van der Schaft, Arjan and Meinsma, Gjerrit},
  year={2002},
  pages={371--385}
}

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