On Higher-order Linear Port-Hamiltonian Systems and Their Duals

Authors

P. Rapisarda, J.C. Mayo Maldonado

Abstract

We formulate a behavioral approach to higher-order linear port-Hamiltonian systems. We formalize constitutive laws such as power conservation, storage and (anti-)dissipative relations, and we study several properties of such systems. We also define the dual of a given port-Hamiltonian behavior.

Keywords

Bilinear-; quadratic differential forms; port-Hamiltonian systems; behavioral system theory; duality; switched linear differential systems

Citation

• Journal: IFAC-PapersOnLine
• Year: 2017
• Volume: 50
• Issue: 1
• Pages: 9236–9241
• Publisher: Elsevier BV
• DOI: 10.1016/j.ifacol.2017.08.1283
• Note: 20th IFAC World Congress

BibTeX

@article{Rapisarda_2017,
  title={{On Higher-order Linear Port-Hamiltonian Systems and Their Duals}},
  volume={50},
  ISSN={2405-8963},
  DOI={10.1016/j.ifacol.2017.08.1283},
  number={1},
  journal={IFAC-PapersOnLine},
  publisher={Elsevier BV},
  author={Rapisarda, P. and Maldonado, J.C. Mayo},
  year={2017},
  pages={9236--9241}
}

Download the bib file

References

• Ardakanian, O. et al. Event detection and localization in distribution grids with phasor measurement units. 2017 IEEE Power & Energy Society General Meeting 1–5 (2017) doi:10.1109/pesgm.2017.8273895 – 10.1109/pesgm.2017.8273895
• Coppel, Linear Systems. (1972)
• Duindam, (2009)
• Mayo-Maldonado, J. C. & Rapisarda, P. On positive-realness and stability of switched linear differential systems. 52nd IEEE Conference on Decision and Control 162–167 (2013) doi:10.1109/cdc.2013.6759876 – 10.1109/cdc.2013.6759876
• Mayo-Maldonado, J. C. & Rapisarda, P. Dissipative Switched Linear Differential Systems. IEEE Transactions on Automatic Control vol. 61 3813–3825 (2016) – 10.1109/tac.2016.2520948
• Mayo-Maldonado, J. C. & Rapisarda, P. On Positive-Realness and Lyapunov Functions for Switched Linear Differential Systems. IEEE Transactions on Automatic Control vol. 61 2239–2244 (2016) – 10.1109/tac.2015.2484329
• Mayo-Maldonado, J. C., Rapisarda, P. & Rocha, P. Stability of Switched Linear Differential Systems. IEEE Transactions on Automatic Control vol. 59 2038–2051 (2014) – 10.1109/tac.2014.2314521
• Mazloum, Y., Sayah, H. & Nemer, M. Static and Dynamic Modeling Comparison of an Adiabatic Compressed Air Energy Storage System. Journal of Energy Resources Technology vol. 138 (2016) – 10.1115/1.4033399
• Ortega, R., van der Schaft, A., Maschke, B. & Escobar, G. Interconnection and damping assignment passivity-based control of port-controlled Hamiltonian systems. Automatica vol. 38 585–596 (2002) – 10.1016/s0005-1098(01)00278-3
• Polderman, (1997)
• Raju, M. & Kumar Khaitan, S. Modeling and simulation of compressed air storage in caverns: A case study of the Huntorf plant. Applied Energy vol. 89 474–481 (2012) – 10.1016/j.apenergy.2011.08.019
• Rapisarda, P. & Willems, J. C. State Maps for Linear Systems. SIAM Journal on Control and Optimization vol. 35 1053–1091 (1997) – 10.1137/s0363012994268412
• Rocha, P., Willems, J. C., Rapisarda, P. & Napp, D. On the stability of switched behavioral systems. IEEE Conference on Decision and Control and European Control Conference 1534–1538 (2011) doi:10.1109/cdc.2011.6160860 – 10.1109/cdc.2011.6160860
• Trentelman, H. L. & Willems, J. C. Every storage function is a state function. Systems & Control Letters vol. 32 249–259 (1997) – 10.1016/s0167-6911(97)00081-9
• van der Schaft, A. & Rapisarda, P. State Maps from Integration by Parts. SIAM Journal on Control and Optimization vol. 49 2415–2439 (2011) – 10.1137/100806825
• van der Schaft, A. J. & Camlibel, M. K. A state transfer principle for switching port-Hamiltonian systems. Proceedings of the 48h IEEE Conference on Decision and Control (CDC) held jointly with 2009 28th Chinese Control Conference 45–50 (2009) doi:10.1109/cdc.2009.5400785 – 10.1109/cdc.2009.5400785
• van der Schaft, Port-Hamiltonian Systems Theory: An Introductory Overview. (2014)
• Willems, J. The Behavioral Approach to Open and Interconnected Systems. IEEE Control Systems Magazine vol. 27 x1–x1 (2007) – 10.1109/mcs.2007.4339280
• Willems, J. Terminals and Ports. IEEE Circuits and Systems Magazine vol. 10 8–26 (2010) – 10.1109/mcas.2010.938635
• Willems, J. C. & Trentelman, H. L. On Quadratic Differential Forms. SIAM Journal on Control and Optimization vol. 36 1703–1749 (1998) – 10.1137/s0363012996303062
• Willems, J. C. & Trentelman, H. L. Synthesis of dissipative systems using quadratic differential forms: Part I. IEEE Transactions on Automatic Control vol. 47 53–69 (2002) – 10.1109/9.981722
• Wing, (2008)