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, and the European Control Conference, CDC-ECC '05

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

doi:10.1109/CDC.2005.1582987

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, and the European Control Conference, CDC-ECC '05

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

Research output: Contribution to conference › Paper › peer-review

1 Scopus citations

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. © 2005 IEEE.

Original language	British English
Pages	5198-5203
Number of pages	6
DOIs	https://doi.org/10.1109/CDC.2005.1582987
State	Published - 2005

Keywords

Discrete time control systems
Equivalent circuits
Feedback control
System stability
Double-sided inputs
Feedback systems
Self-consistency
Nonlinear control systems

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10.1109/CDC.2005.1582987

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title = "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, and the European Control Conference, CDC-ECC '05",

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. {\textcopyright} 2005 IEEE.",

keywords = "Discrete time control systems, Equivalent circuits, Feedback control, System stability, Double-sided inputs, Feedback systems, Self-consistency, Nonlinear control systems",

author = "W.E. Leithead and E. Ragnoli and J. O'Reilly",

note = "Export Date: 29 November 2023; Cited By: 1; Correspondence Address: W.E. Leithead; Hamilton Institute, NUIM, Maynooth, Co., Kildare, Ireland; email: [email protected]; Conference name: 44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05; Conference date: 12 December 2005 through 15 December 2005; Conference code: 69208",

year = "2005",

doi = "10.1109/CDC.2005.1582987",

language = "British English",

pages = "5198--5203",

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T2 - Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05

AU - Leithead, W.E.

AU - Ragnoli, E.

AU - O'Reilly, J.

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AB - 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. © 2005 IEEE.

KW - Discrete time control systems

KW - Equivalent circuits

KW - Feedback control

KW - System stability

KW - Double-sided inputs

KW - Feedback systems

KW - Self-consistency

KW - Nonlinear control systems

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