Open-loop unstable feedback systems with double-sided inputs: an explicit demonstration of self-consistency

W.E. Leithead, E. Ragnoli, J. O'Reilly

Research output: Chapter in Book/Report/Conference proceedingConference contribution book

1 Citation (Scopus)

Abstract

The standard formulation of linear shift-invariant feedback systems in the doubly infinite time axis setting lacks self-consistency with seemingly irreconcilable difficulties having been identified when the system is open-loop unstable. The available options for circumventing these difficulties for discrete-time SISO systems are highlighted and the manner in which they are exploited to obtain a self-consistent framework by reformulating the feedback systems in the space of distributions is clarified. In addition, it is explicitly demonstrated that causality and stability of a standard example are implied by the causality and stability of the equivalent system when reformulated in the self-consistent framework.
LanguageEnglish
Title of host publicationProceedings of the 44th IEEE Conference on Decision and Control, 2005 and 2005 European Control Conference
Subtitle of host publicationCDC-ECC '05
PublisherIEEE
Pages5198-5203
Number of pages6
ISBN (Print)0-7803-9567-0
DOIs
Publication statusPublished - Dec 2005
Event44th IEEE Conference on Decision and Control and European Control Conference - Seville, Spain
Duration: 12 Dec 200515 Dec 2005

Conference

Conference44th IEEE Conference on Decision and Control and European Control Conference
Abbreviated titleCDC-ECC
CountrySpain
CitySeville
Period12/12/0515/12/05

Fingerprint

Demonstrations
Feedback
Open systems

Keywords

  • control systems
  • control theory
  • feedback loops
  • open loop systems
  • signal analysis

Cite this

Leithead, W. E., Ragnoli, E., & O'Reilly, J. (2005). Open-loop unstable feedback systems with double-sided inputs: an explicit demonstration of self-consistency. In Proceedings of the 44th IEEE Conference on Decision and Control, 2005 and 2005 European Control Conference: CDC-ECC '05 (pp. 5198-5203). IEEE. https://doi.org/10.1109/CDC.2005.1582987
Leithead, W.E. ; Ragnoli, E. ; O'Reilly, J. / Open-loop unstable feedback systems with double-sided inputs : an explicit demonstration of self-consistency. Proceedings of the 44th IEEE Conference on Decision and Control, 2005 and 2005 European Control Conference: CDC-ECC '05. IEEE, 2005. pp. 5198-5203
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abstract = "The standard formulation of linear shift-invariant feedback systems in the doubly infinite time axis setting lacks self-consistency with seemingly irreconcilable difficulties having been identified when the system is open-loop unstable. The available options for circumventing these difficulties for discrete-time SISO systems are highlighted and the manner in which they are exploited to obtain a self-consistent framework by reformulating the feedback systems in the space of distributions is clarified. In addition, it is explicitly demonstrated that causality and stability of a standard example are implied by the causality and stability of the equivalent system when reformulated in the self-consistent framework.",
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Leithead, WE, Ragnoli, E & O'Reilly, J 2005, Open-loop unstable feedback systems with double-sided inputs: an explicit demonstration of self-consistency. in Proceedings of the 44th IEEE Conference on Decision and Control, 2005 and 2005 European Control Conference: CDC-ECC '05. IEEE, pp. 5198-5203, 44th IEEE Conference on Decision and Control and European Control Conference , Seville, Spain, 12/12/05. https://doi.org/10.1109/CDC.2005.1582987

Open-loop unstable feedback systems with double-sided inputs : an explicit demonstration of self-consistency. / Leithead, W.E.; Ragnoli, E.; O'Reilly, J.

Proceedings of the 44th IEEE Conference on Decision and Control, 2005 and 2005 European Control Conference: CDC-ECC '05. IEEE, 2005. p. 5198-5203.

Research output: Chapter in Book/Report/Conference proceedingConference contribution book

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Leithead WE, Ragnoli E, O'Reilly J. Open-loop unstable feedback systems with double-sided inputs: an explicit demonstration of self-consistency. In Proceedings of the 44th IEEE Conference on Decision and Control, 2005 and 2005 European Control Conference: CDC-ECC '05. IEEE. 2005. p. 5198-5203 https://doi.org/10.1109/CDC.2005.1582987