Conditions on shifted passivity of port-Hamiltonian systems

Authors

Nima Monshizadeh, Pooya Monshizadeh, Romeo Ortega, Arjan van der Schaft

Abstract

In this paper, we examine the shifted passivity property of port-Hamiltonian systems. Shifted passivity accounts for the fact that in many applications the desired steady-state values of the input and output variables are nonzero, and thus one is interested in passivity with respect to the shifted signals. We consider port-Hamiltonian systems with strictly convex Hamiltonian, and derive conditions under which shifted passivity is guaranteed. In case the Hamiltonian is quadratic and state dependency appears in an affine manner in the dissipation and interconnection matrices, our conditions reduce to negative semidefiniteness of an appropriately constructed constant matrix. Moreover, we elaborate on how these conditions can be extended to the case when the shifted passivity property can be enforced via output feedback, thus paving the path for controller design. Stability of forced equilibria of the system is analyzed invoking the proposed passivity conditions. The utility and relevance of the results are illustrated with their application to a 6th order synchronous generator model as well as a controlled rigid body system.

Keywords

incremental passivity, passivity, port-hamiltonian systems, shifted passivity, stability theory

Citation

Journal: Systems & Control Letters
Year: 2019
Volume: 123
Issue:
Pages: 55–61
Publisher: Elsevier BV
DOI: 10.1016/j.sysconle.2018.10.010

BibTeX

@article{Monshizadeh_2019,
  title={{Conditions on shifted passivity of port-Hamiltonian systems}},
  volume={123},
  ISSN={0167-6911},
  DOI={10.1016/j.sysconle.2018.10.010},
  journal={Systems \&amp; Control Letters},
  publisher={Elsevier BV},
  author={Monshizadeh, Nima and Monshizadeh, Pooya and Ortega, Romeo and van der Schaft, Arjan},
  year={2019},
  pages={55--61}
}

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