Hamiltonian approach to the stabilization of systems of two conservation laws

Authors

V. Dos Santos Martins, B. Maschke, Y. Le Gorrec

Abstract

This paper aims at providing some synthesis between two alternative representations of systems of two conservation laws and interprets different conditions on stabilizing boundary control laws. The first is the representation in Riemann invariants coordinates whose representation has been applied successfully for the stabilization of linear and non-linear of such hyperbolic systems. The second representation is based on physical modelling and leads to port Hamiltonian systems which are extensions of infinite-dimensional Hamiltonian systems defined on Dirac structure. The stability conditions on the boundary feedback relations derived with respect to the Riemann invariants are interpreted in terms of the dissipation inequality of the Hamiltonian functional.

Keywords

boundary port hamiltonian systems, distributed parameters systems, stability

Citation

• Journal: IFAC Proceedings Volumes
• Year: 2010
• Volume: 43
• Issue: 14
• Pages: 581–586
• Publisher: Elsevier BV
• DOI: 10.3182/20100901-3-it-2016.00095
• Note: 8th IFAC Symposium on Nonlinear Control Systems

BibTeX

@article{Martins_2010,
  title={{Hamiltonian approach to the stabilization of systems of two conservation laws}},
  volume={43},
  ISSN={1474-6670},
  DOI={10.3182/20100901-3-it-2016.00095},
  number={14},
  journal={IFAC Proceedings Volumes},
  publisher={Elsevier BV},
  author={Martins, V. Dos Santos and Maschke, B. and Gorrec, Y. Le},
  year={2010},
  pages={581--586}
}

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