On the nonexistence of limit cycles for a class of nonlinear systems under parameter uncertainties

Pingli Lu; Ying Yang; Lin Huang

doi:10.1109/ACC.2007.4282516

On the nonexistence of limit cycles for a class of nonlinear systems under parameter uncertainties

Pingli Lu^*, Ying Yang, Lin Huang

^*Corresponding author for this work

Peking University

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

Abstract

This paper concerns the nonexistence of limit cycles in a class of nonlinear systems which are subject to norm-bounded parameter uncertainty in the state and input matrices. Based on Kalman-Yakubovich-Popov (KYP) lemma, sufficient conditions for the nonexistence of limit cycles in such uncertain nonlinear systems are derived in terms of linear matrix inequalities(LMIs) and an efficient way for estimation of the uncertainty bound is proposed by solving a generalized eigenvalue minimization problem. Based on the results, static state feedback controller and dynamic output feedback controller are designed ensuring the closed-loop uncertain nonlinear system has no limit cycles respectively. A concrete application to Chua's circuit shows the applicability of the proposed approach.

Original language	English
Title of host publication	Proceedings of the 2007 American Control Conference, ACC
Pages	3059-3064
Number of pages	6
DOIs	https://doi.org/10.1109/ACC.2007.4282516
Publication status	Published - 2007
Externally published	Yes
Event	2007 American Control Conference, ACC - New York, NY, United States Duration: 9 Jul 2007 → 13 Jul 2007

Publication series

Name	Proceedings of the American Control Conference
ISSN (Print)	0743-1619

Conference

Conference	2007 American Control Conference, ACC
Country/Territory	United States
City	New York, NY
Period	9/07/07 → 13/07/07

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10.1109/ACC.2007.4282516

Cite this

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title = "On the nonexistence of limit cycles for a class of nonlinear systems under parameter uncertainties",

abstract = "This paper concerns the nonexistence of limit cycles in a class of nonlinear systems which are subject to norm-bounded parameter uncertainty in the state and input matrices. Based on Kalman-Yakubovich-Popov (KYP) lemma, sufficient conditions for the nonexistence of limit cycles in such uncertain nonlinear systems are derived in terms of linear matrix inequalities(LMIs) and an efficient way for estimation of the uncertainty bound is proposed by solving a generalized eigenvalue minimization problem. Based on the results, static state feedback controller and dynamic output feedback controller are designed ensuring the closed-loop uncertain nonlinear system has no limit cycles respectively. A concrete application to Chua's circuit shows the applicability of the proposed approach.",

author = "Pingli Lu and Ying Yang and Lin Huang",

year = "2007",

doi = "10.1109/ACC.2007.4282516",

language = "English",

isbn = "1424409888",

series = "Proceedings of the American Control Conference",

pages = "3059--3064",

booktitle = "Proceedings of the 2007 American Control Conference, ACC",

note = "2007 American Control Conference, ACC ; Conference date: 09-07-2007 Through 13-07-2007",

}

Lu, P, Yang, Y & Huang, L 2007, On the nonexistence of limit cycles for a class of nonlinear systems under parameter uncertainties. in Proceedings of the 2007 American Control Conference, ACC., 4282516, Proceedings of the American Control Conference, pp. 3059-3064, 2007 American Control Conference, ACC, New York, NY, United States, 9/07/07. https://doi.org/10.1109/ACC.2007.4282516

On the nonexistence of limit cycles for a class of nonlinear systems under parameter uncertainties. / Lu, Pingli; Yang, Ying; Huang, Lin.
Proceedings of the 2007 American Control Conference, ACC. 2007. p. 3059-3064 4282516 (Proceedings of the American Control Conference).

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

TY - GEN

T1 - On the nonexistence of limit cycles for a class of nonlinear systems under parameter uncertainties

AU - Lu, Pingli

AU - Yang, Ying

AU - Huang, Lin

PY - 2007

Y1 - 2007

N2 - This paper concerns the nonexistence of limit cycles in a class of nonlinear systems which are subject to norm-bounded parameter uncertainty in the state and input matrices. Based on Kalman-Yakubovich-Popov (KYP) lemma, sufficient conditions for the nonexistence of limit cycles in such uncertain nonlinear systems are derived in terms of linear matrix inequalities(LMIs) and an efficient way for estimation of the uncertainty bound is proposed by solving a generalized eigenvalue minimization problem. Based on the results, static state feedback controller and dynamic output feedback controller are designed ensuring the closed-loop uncertain nonlinear system has no limit cycles respectively. A concrete application to Chua's circuit shows the applicability of the proposed approach.

AB - This paper concerns the nonexistence of limit cycles in a class of nonlinear systems which are subject to norm-bounded parameter uncertainty in the state and input matrices. Based on Kalman-Yakubovich-Popov (KYP) lemma, sufficient conditions for the nonexistence of limit cycles in such uncertain nonlinear systems are derived in terms of linear matrix inequalities(LMIs) and an efficient way for estimation of the uncertainty bound is proposed by solving a generalized eigenvalue minimization problem. Based on the results, static state feedback controller and dynamic output feedback controller are designed ensuring the closed-loop uncertain nonlinear system has no limit cycles respectively. A concrete application to Chua's circuit shows the applicability of the proposed approach.

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M3 - Conference contribution

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SN - 9781424409884

T3 - Proceedings of the American Control Conference

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BT - Proceedings of the 2007 American Control Conference, ACC

T2 - 2007 American Control Conference, ACC

Y2 - 9 July 2007 through 13 July 2007

ER -

On the nonexistence of limit cycles for a class of nonlinear systems under parameter uncertainties

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