Authors

H. Zwart, Y. Le Gorrec, B. Maschke

Abstract

In this article we introduce a technique that derives from the existence and uniqueness of solutions to a simple hyperbolic partial differential equation (p.d.e.) the existence and uniqueness of solutions to hyperbolic and parabolic p.d.e.’s. Among others, we show that starting with an impedance passive system associated to the undamped wave equation, we can obtain an impedance passive system associated to the heat conduction equation.

Keywords

impedance passive, infinite-dimensional systems theory, partial differential equation

Citation

BibTeX

@article{Zwart_2016,
  title={{Building systems from simple hyperbolic ones}},
  volume={91},
  ISSN={0167-6911},
  DOI={10.1016/j.sysconle.2016.02.002},
  journal={Systems \& Control Letters},
  publisher={Elsevier BV},
  author={Zwart, H. and Le Gorrec, Y. and Maschke, B.},
  year={2016},
  pages={1--6}
}

Download the bib file

References

  • Curtain, (1995)
  • Staffans, (2005)
  • Duindam, (2009)
  • Staffans OJ, Weiss G (2012) A Physically Motivated Class of Scattering Passive Linear Systems. SIAM J Control Optim 50(5):3083–3112. https://doi.org/10.1137/11084640 – 10.1137/110846403
  • Weiss G, Staffans OJ (2013) Maxwell’s Equations as a Scattering Passive Linear System. SIAM J Control Optim 51(5):3722–3756. https://doi.org/10.1137/12086944 – 10.1137/120869444
  • Kurula M, Zwart H (2016) Feedback theory extended for proving generation of contraction semigroups. J Evol Equ 16(3):617–647. https://doi.org/10.1007/s00028-015-0315- – 10.1007/s00028-015-0315-1
  • Engel, (2000)
  • Jacob, (2012)
  • Villegas, (2007)
  • Staffans OJ (2002) Passive and Conservative Continuous-Time Impedance and Scattering Systems. Part I: Well-Posed Systems. Mathematics of Control, Signals, and Systems (MCSS) 15(4):291–315. https://doi.org/10.1007/s00498020001 – 10.1007/s004980200012
  • Zwart H, Gorrec YL, Maschke B (2015) Relating systems properties of the wave and the Schrödinger equation. EECT 4(2):233–240. https://doi.org/10.3934/eect.2015.4.23 – 10.3934/eect.2015.4.233
  • Schwenninger FL, Zwart H (2014) Generators with a closure relation. Operators and Matrices (1):157–165. https://doi.org/10.7153/oam-08-0 – 10.7153/oam-08-08