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

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

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

Electronic And Electrical Engineering

Research output: Chapter in Book/Report/Conference proceeding › Conference 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.

Original language	English
Title of host publication	Proceedings of the 44th IEEE Conference on Decision and Control, 2005 and 2005 European Control Conference
Subtitle of host publication	CDC-ECC '05
Publisher	IEEE
Pages	5198-5203
Number of pages	6
ISBN (Print)	0-7803-9567-0
DOIs	https://doi.org/10.1109/CDC.2005.1582987
Publication status	Published - Dec 2005
Event	44th IEEE Conference on Decision and Control and European Control Conference - Seville, Spain Duration: 12 Dec 2005 → 15 Dec 2005

Conference

Conference	44th IEEE Conference on Decision and Control and European Control Conference
Abbreviated title	CDC-ECC
Country/Territory	Spain
City	Seville
Period	12/12/05 → 15/12/05

Keywords

control systems
control theory
feedback loops
open loop systems
signal analysis

Access to Document

10.1109/CDC.2005.1582987

Cite this

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

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.",

keywords = "control systems, control theory, feedback loops, open loop systems, signal analysis",

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

year = "2005",

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doi = "10.1109/CDC.2005.1582987",

language = "English",

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pages = "5198--5203",

booktitle = "Proceedings of the 44th IEEE Conference on Decision and Control, 2005 and 2005 European Control Conference",

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note = "44th IEEE Conference on Decision and Control and European Control Conference , CDC-ECC ; Conference date: 12-12-2005 Through 15-12-2005",

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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 proceeding › Conference contribution book

TY - GEN

T1 - Open-loop unstable feedback systems with double-sided inputs

T2 - 44th IEEE Conference on Decision and Control and European Control Conference

AU - Leithead, W.E.

AU - Ragnoli, E.

AU - O'Reilly, J.

PY - 2005/12

Y1 - 2005/12

N2 - 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.

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.

KW - control systems

KW - control theory

KW - feedback loops

KW - open loop systems

KW - signal analysis

U2 - 10.1109/CDC.2005.1582987

DO - 10.1109/CDC.2005.1582987

M3 - Conference contribution book

SN - 0-7803-9567-0

SP - 5198

EP - 5203

BT - Proceedings of the 44th IEEE Conference on Decision and Control, 2005 and 2005 European Control Conference

PB - IEEE

Y2 - 12 December 2005 through 15 December 2005

ER -

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

Abstract

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Keywords

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