Global asymptotic stability of pendulum-like system with state delay

Pingli Lu; Ying Yang; Lin Huang

doi:10.1109/CDC.2007.4434305

Global asymptotic stability of pendulum-like system with state delay

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

1 Citation (Scopus)

Abstract

This paper considers robust global asymptotic stability for the delayed nonlinear pendulum-like systems with ploytopic uncertainties. The delay-dependent criteria, guaranteeing the global asymptotic stability for the pendulum-like systems with state delay, for the first time, are established in terms of linear matrix inequalities (LMIs) which can be checked by resorting to recently developed algorithms solving LMIs. Furthermore, based on the derived delay-dependent global asymptotic stability results, LMI characterizations are developed to ensure the robust global asymptotic stability for delayed pendulum-like systems under convex polytopic uncertainties. The new extended LMIs involve no product of the Lyapunov matrix and the system matrices. It enables one to check the global asymptotic stability by using parameter-dependent Lyapunov methods. Finally, a concrete application to phase-locked loop (PLL) illustrates the validity of the proposed approach.

Original language	English
Title of host publication	Proceedings of the 46th IEEE Conference on Decision and Control 2007, CDC
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	2229-2234
Number of pages	6
ISBN (Print)	1424414989, 9781424414987
DOIs	https://doi.org/10.1109/CDC.2007.4434305
Publication status	Published - 2007
Externally published	Yes
Event	46th IEEE Conference on Decision and Control 2007, CDC - New Orleans, LA, United States Duration: 12 Dec 2007 → 14 Dec 2007

Publication series

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

Conference

Conference	46th IEEE Conference on Decision and Control 2007, CDC
Country/Territory	United States
City	New Orleans, LA
Period	12/12/07 → 14/12/07

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10.1109/CDC.2007.4434305

Cite this

Lu, P., Yang, Y., & Huang, L. (2007). Global asymptotic stability of pendulum-like system with state delay. In Proceedings of the 46th IEEE Conference on Decision and Control 2007, CDC (pp. 2229-2234). Article 4434305 (Proceedings of the IEEE Conference on Decision and Control). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/CDC.2007.4434305

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title = "Global asymptotic stability of pendulum-like system with state delay",

abstract = "This paper considers robust global asymptotic stability for the delayed nonlinear pendulum-like systems with ploytopic uncertainties. The delay-dependent criteria, guaranteeing the global asymptotic stability for the pendulum-like systems with state delay, for the first time, are established in terms of linear matrix inequalities (LMIs) which can be checked by resorting to recently developed algorithms solving LMIs. Furthermore, based on the derived delay-dependent global asymptotic stability results, LMI characterizations are developed to ensure the robust global asymptotic stability for delayed pendulum-like systems under convex polytopic uncertainties. The new extended LMIs involve no product of the Lyapunov matrix and the system matrices. It enables one to check the global asymptotic stability by using parameter-dependent Lyapunov methods. Finally, a concrete application to phase-locked loop (PLL) illustrates the validity of the proposed approach.",

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

year = "2007",

doi = "10.1109/CDC.2007.4434305",

language = "English",

isbn = "1424414989",

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

publisher = "Institute of Electrical and Electronics Engineers Inc.",

pages = "2229--2234",

booktitle = "Proceedings of the 46th IEEE Conference on Decision and Control 2007, CDC",

address = "United States",

note = "46th IEEE Conference on Decision and Control 2007, CDC ; Conference date: 12-12-2007 Through 14-12-2007",

}

Lu, P, Yang, Y & Huang, L 2007, Global asymptotic stability of pendulum-like system with state delay. in Proceedings of the 46th IEEE Conference on Decision and Control 2007, CDC., 4434305, Proceedings of the IEEE Conference on Decision and Control, Institute of Electrical and Electronics Engineers Inc., pp. 2229-2234, 46th IEEE Conference on Decision and Control 2007, CDC, New Orleans, LA, United States, 12/12/07. https://doi.org/10.1109/CDC.2007.4434305

Global asymptotic stability of pendulum-like system with state delay. / Lu, Pingli; Yang, Ying; Huang, Lin.
Proceedings of the 46th IEEE Conference on Decision and Control 2007, CDC. Institute of Electrical and Electronics Engineers Inc., 2007. p. 2229-2234 4434305 (Proceedings of the IEEE Conference on Decision and Control).

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

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AU - Lu, Pingli

AU - Yang, Ying

AU - Huang, Lin

PY - 2007

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N2 - This paper considers robust global asymptotic stability for the delayed nonlinear pendulum-like systems with ploytopic uncertainties. The delay-dependent criteria, guaranteeing the global asymptotic stability for the pendulum-like systems with state delay, for the first time, are established in terms of linear matrix inequalities (LMIs) which can be checked by resorting to recently developed algorithms solving LMIs. Furthermore, based on the derived delay-dependent global asymptotic stability results, LMI characterizations are developed to ensure the robust global asymptotic stability for delayed pendulum-like systems under convex polytopic uncertainties. The new extended LMIs involve no product of the Lyapunov matrix and the system matrices. It enables one to check the global asymptotic stability by using parameter-dependent Lyapunov methods. Finally, a concrete application to phase-locked loop (PLL) illustrates the validity of the proposed approach.

AB - This paper considers robust global asymptotic stability for the delayed nonlinear pendulum-like systems with ploytopic uncertainties. The delay-dependent criteria, guaranteeing the global asymptotic stability for the pendulum-like systems with state delay, for the first time, are established in terms of linear matrix inequalities (LMIs) which can be checked by resorting to recently developed algorithms solving LMIs. Furthermore, based on the derived delay-dependent global asymptotic stability results, LMI characterizations are developed to ensure the robust global asymptotic stability for delayed pendulum-like systems under convex polytopic uncertainties. The new extended LMIs involve no product of the Lyapunov matrix and the system matrices. It enables one to check the global asymptotic stability by using parameter-dependent Lyapunov methods. Finally, a concrete application to phase-locked loop (PLL) illustrates the validity of the proposed approach.

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SN - 9781424414987

T3 - Proceedings of the IEEE Conference on Decision and Control

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Global asymptotic stability of pendulum-like system with state delay

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