A pseudo-H∞ control theory and its application to the control of pendulum-like nonlinear systems

Hua Ouyang; Ian R. Petersen; Valery Ugrinovskii

doi:10.1109/CDC.2009.5399686

A pseudo-H_∞ control theory and its application to the control of pendulum-like nonlinear systems

Hua Ouyang^*
, Ian R. Petersen
, Valery Ugrinovskii

^*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceeding › Conference Paper › peer-review

2 Citations (Scopus)

Abstract

This paper studies the problem of control of pendulum-like nonlinear systems to achieve closed-loop Lagrange stability. A state feedback pseudo-H_∞ control theory is developed. In a similar fashion to the strict bounded real lemma in H_∞ control theory, a strict pseudo-bounded real lemma is established. A sufficient condition for the synthesis of the state feedback pseudo-H_∞ control is given, which is also applied to the control of pendulum-like nonlinear systems.

Original language	English
Title of host publication	Proceedings of the 48th IEEE Conference on Decision and Control held jointly with 2009 28th Chinese Control Conference, CDC/CCC 2009
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	2125-2131
Number of pages	7
ISBN (Print)	9781424438716
DOIs	https://doi.org/10.1109/CDC.2009.5399686
Publication status	Published - 2009
Externally published	Yes
Event	48th IEEE Conference on Decision and Control held jointly with 2009 28th Chinese Control Conference, CDC/CCC 2009 - Shanghai, China Duration: 15 Dec 2009 → 18 Dec 2009

Publication series

Name	Proceedings of the IEEE Conference on Decision and Control
ISSN (Print)	0743-1546
ISSN (Electronic)	2576-2370

Conference

Conference	48th IEEE Conference on Decision and Control held jointly with 2009 28th Chinese Control Conference, CDC/CCC 2009
Country/Territory	China
City	Shanghai
Period	15/12/09 → 18/12/09

Access to Document

10.1109/CDC.2009.5399686

Cite this

Ouyang, H., Petersen, I. R., & Ugrinovskii, V. (2009). A pseudo-H_∞ control theory and its application to the control of pendulum-like nonlinear systems. In Proceedings of the 48th IEEE Conference on Decision and Control held jointly with 2009 28th Chinese Control Conference, CDC/CCC 2009 (pp. 2125-2131). Article 5399686 (Proceedings of the IEEE Conference on Decision and Control). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/CDC.2009.5399686

Ouyang, Hua ; Petersen, Ian R. ; Ugrinovskii, Valery. / A pseudo-H_∞ control theory and its application to the control of pendulum-like nonlinear systems. Proceedings of the 48th IEEE Conference on Decision and Control held jointly with 2009 28th Chinese Control Conference, CDC/CCC 2009. Institute of Electrical and Electronics Engineers Inc., 2009. pp. 2125-2131 (Proceedings of the IEEE Conference on Decision and Control).

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title = "A pseudo-H∞ control theory and its application to the control of pendulum-like nonlinear systems",

abstract = "This paper studies the problem of control of pendulum-like nonlinear systems to achieve closed-loop Lagrange stability. A state feedback pseudo-H∞ control theory is developed. In a similar fashion to the strict bounded real lemma in H∞ control theory, a strict pseudo-bounded real lemma is established. A sufficient condition for the synthesis of the state feedback pseudo-H∞ control is given, which is also applied to the control of pendulum-like nonlinear systems.",

keywords = "Lagrange stability, Pendulum-like nonlinear system, Strict Pseudo-bounded real lemma",

author = "Hua Ouyang and Petersen, \{Ian R.\} and Valery Ugrinovskii",

year = "2009",

doi = "10.1109/CDC.2009.5399686",

language = "English",

isbn = "9781424438716",

series = "Proceedings of the IEEE Conference on Decision and Control",

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pages = "2125--2131",

booktitle = "Proceedings of the 48th IEEE Conference on Decision and Control held jointly with 2009 28th Chinese Control Conference, CDC/CCC 2009",

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note = "48th IEEE Conference on Decision and Control held jointly with 2009 28th Chinese Control Conference, CDC/CCC 2009 ; Conference date: 15-12-2009 Through 18-12-2009",

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Ouyang, H, Petersen, IR & Ugrinovskii, V 2009, A pseudo-H_∞ control theory and its application to the control of pendulum-like nonlinear systems. in Proceedings of the 48th IEEE Conference on Decision and Control held jointly with 2009 28th Chinese Control Conference, CDC/CCC 2009., 5399686, Proceedings of the IEEE Conference on Decision and Control, Institute of Electrical and Electronics Engineers Inc., pp. 2125-2131, 48th IEEE Conference on Decision and Control held jointly with 2009 28th Chinese Control Conference, CDC/CCC 2009, Shanghai, China, 15/12/09. https://doi.org/10.1109/CDC.2009.5399686

A pseudo-H_∞ control theory and its application to the control of pendulum-like nonlinear systems. / Ouyang, Hua; Petersen, Ian R.; Ugrinovskii, Valery.
Proceedings of the 48th IEEE Conference on Decision and Control held jointly with 2009 28th Chinese Control Conference, CDC/CCC 2009. Institute of Electrical and Electronics Engineers Inc., 2009. p. 2125-2131 5399686 (Proceedings of the IEEE Conference on Decision and Control).

Research output: Chapter in Book/Report/Conference proceeding › Conference Paper › peer-review

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N2 - This paper studies the problem of control of pendulum-like nonlinear systems to achieve closed-loop Lagrange stability. A state feedback pseudo-H∞ control theory is developed. In a similar fashion to the strict bounded real lemma in H∞ control theory, a strict pseudo-bounded real lemma is established. A sufficient condition for the synthesis of the state feedback pseudo-H∞ control is given, which is also applied to the control of pendulum-like nonlinear systems.

AB - This paper studies the problem of control of pendulum-like nonlinear systems to achieve closed-loop Lagrange stability. A state feedback pseudo-H∞ control theory is developed. In a similar fashion to the strict bounded real lemma in H∞ control theory, a strict pseudo-bounded real lemma is established. A sufficient condition for the synthesis of the state feedback pseudo-H∞ control is given, which is also applied to the control of pendulum-like nonlinear systems.

KW - Lagrange stability

KW - Pendulum-like nonlinear system

KW - Strict Pseudo-bounded real lemma

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Ouyang H, Petersen IR, Ugrinovskii V. A pseudo-H_∞ control theory and its application to the control of pendulum-like nonlinear systems. In Proceedings of the 48th IEEE Conference on Decision and Control held jointly with 2009 28th Chinese Control Conference, CDC/CCC 2009. Institute of Electrical and Electronics Engineers Inc. 2009. p. 2125-2131. 5399686. (Proceedings of the IEEE Conference on Decision and Control). doi: 10.1109/CDC.2009.5399686