Authors

Selvaraj Karikalan, Madhu N. Belur, Chirayu D. Athalye, Rihab Abdul Razak

Abstract

The theory of dissipativity is well developed for controllable systems. A more appropriate definition in the context uncontrollable systems terms existence a storage function, namely function such that, along every system trajectory, its rate change at each time instant most power supplied to that time. However, even when expressible just external variables, property crucially hinges on whether or not depends variables unobservable/hidden from variables: this paper investigates key aspects both cases, and also proposes another intuitive dissipativity. These three definitions are compared: we show drawbacks one addressed by another.Dealing first with observable functions, under conditions no two poles add zero strict as frequency tends infinity, prove dissipativities part equivalent. We use behavioural approach formalising notions: behaviour set all trajectories. functions have be unobservable lossless’ It known, however, result certain fallacious’ examples lossless propose an dissipativity: system/behaviour called dissipative if it can embedded superbehaviour. embeddability results them resolve fallacy example termed due functions. next quite unreasonably, admits behaviours strictly antidissipative. Drawbacks RLC circuits finally related inability realise/synthesise special one-port electrical network, nullator, using only passive components.

Citation

  • Journal: International Journal of Control
  • Year: 2014
  • Volume: 87
  • Issue: 1
  • Pages: 101–119
  • Publisher: Informa UK Limited
  • DOI: 10.1080/00207179.2013.823668

BibTeX

@article{Karikalan_2013,
  title={{Uncontrollable dissipative systems: observability and embeddability}},
  volume={87},
  ISSN={1366-5820},
  DOI={10.1080/00207179.2013.823668},
  number={1},
  journal={International Journal of Control},
  publisher={Informa UK Limited},
  author={Karikalan, Selvaraj and Belur, Madhu N. and Athalye, Chirayu D. and Razak, Rihab Abdul},
  year={2013},
  pages={101--119}
}

Download the bib file

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