On strict Lyapunov functions for rapidly time-varying nonlinear systems

Frédéric Mazenc; Michael Malisoff; Marcio S. De Queiroz

doi:10.1109/ACC.2006.1656563

On strict Lyapunov functions for rapidly time-varying nonlinear systems

Frédéric Mazenc
, Michael Malisoff
, Marcio S. De Queiroz

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

Abstract

We explicitly construct Lyapunov functions for rapidly time-varying nonlinear systems. The Lyapunov functions we construct are expressed in terms of oftentimes more readily available Lyapunov functions for the limiting dynamics which we assume are globally asymptotically stable. This leads to new sufficient conditions for global exponential, global asymptotic, and input-to-state stability of fast time-varying dynamics. We apply our results to two examples.

Original language	English
Title of host publication	Proceedings of the 2006 American Control Conference
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	2303-2308
Number of pages	6
ISBN (Print)	1424402107, 9781424402106
DOIs	https://doi.org/10.1109/ACC.2006.1656563
State	Published - 2006
Externally published	Yes
Event	2006 American Control Conference - Minneapolis, MN, United States Duration: Jun 14 2006 → Jun 16 2006

Publication series

Name	Proceedings of the American Control Conference
Volume	2006
ISSN (Print)	0743-1619

Conference

Conference	2006 American Control Conference
Country/Territory	United States
City	Minneapolis, MN
Period	06/14/06 → 06/16/06

Keywords

Input-to-state stability
Lyapunov function constructions
Time-varying systems

Access to Document

10.1109/ACC.2006.1656563

Cite this

Mazenc, F., Malisoff, M., & De Queiroz, M. S. (2006). On strict Lyapunov functions for rapidly time-varying nonlinear systems. In Proceedings of the 2006 American Control Conference (pp. 2303-2308). Article 1656563 (Proceedings of the American Control Conference; Vol. 2006). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/ACC.2006.1656563

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title = "On strict Lyapunov functions for rapidly time-varying nonlinear systems",

abstract = "We explicitly construct Lyapunov functions for rapidly time-varying nonlinear systems. The Lyapunov functions we construct are expressed in terms of oftentimes more readily available Lyapunov functions for the limiting dynamics which we assume are globally asymptotically stable. This leads to new sufficient conditions for global exponential, global asymptotic, and input-to-state stability of fast time-varying dynamics. We apply our results to two examples.",

keywords = "Input-to-state stability, Lyapunov function constructions, Time-varying systems",

author = "Fr{\'e}d{\'e}ric Mazenc and Michael Malisoff and \{De Queiroz\}, \{Marcio S.\}",

year = "2006",

doi = "10.1109/ACC.2006.1656563",

language = "English",

isbn = "1424402107",

series = "Proceedings of the American Control Conference",

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

pages = "2303--2308",

booktitle = "Proceedings of the 2006 American Control Conference",

note = "2006 American Control Conference ; Conference date: 14-06-2006 Through 16-06-2006",

}

Mazenc, F, Malisoff, M & De Queiroz, MS 2006, On strict Lyapunov functions for rapidly time-varying nonlinear systems. in Proceedings of the 2006 American Control Conference., 1656563, Proceedings of the American Control Conference, vol. 2006, Institute of Electrical and Electronics Engineers Inc., pp. 2303-2308, 2006 American Control Conference, Minneapolis, MN, United States, 06/14/06. https://doi.org/10.1109/ACC.2006.1656563

On strict Lyapunov functions for rapidly time-varying nonlinear systems. / Mazenc, Frédéric; Malisoff, Michael; De Queiroz, Marcio S.
Proceedings of the 2006 American Control Conference. Institute of Electrical and Electronics Engineers Inc., 2006. p. 2303-2308 1656563 (Proceedings of the American Control Conference; Vol. 2006).

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

TY - GEN

T1 - On strict Lyapunov functions for rapidly time-varying nonlinear systems

AU - Mazenc, Frédéric

AU - Malisoff, Michael

AU - De Queiroz, Marcio S.

PY - 2006

Y1 - 2006

N2 - We explicitly construct Lyapunov functions for rapidly time-varying nonlinear systems. The Lyapunov functions we construct are expressed in terms of oftentimes more readily available Lyapunov functions for the limiting dynamics which we assume are globally asymptotically stable. This leads to new sufficient conditions for global exponential, global asymptotic, and input-to-state stability of fast time-varying dynamics. We apply our results to two examples.

AB - We explicitly construct Lyapunov functions for rapidly time-varying nonlinear systems. The Lyapunov functions we construct are expressed in terms of oftentimes more readily available Lyapunov functions for the limiting dynamics which we assume are globally asymptotically stable. This leads to new sufficient conditions for global exponential, global asymptotic, and input-to-state stability of fast time-varying dynamics. We apply our results to two examples.

KW - Input-to-state stability

KW - Lyapunov function constructions

KW - Time-varying systems

UR - https://www.scopus.com/pages/publications/34047228879

U2 - 10.1109/ACC.2006.1656563

DO - 10.1109/ACC.2006.1656563

M3 - Conference contribution

AN - SCOPUS:34047228879

SN - 1424402107

SN - 9781424402106

T3 - Proceedings of the American Control Conference

SP - 2303

EP - 2308

BT - Proceedings of the 2006 American Control Conference

PB - Institute of Electrical and Electronics Engineers Inc.

T2 - 2006 American Control Conference

Y2 - 14 June 2006 through 16 June 2006

ER -

On strict Lyapunov functions for rapidly time-varying nonlinear systems

Abstract

Publication series

Conference

Keywords

Access to Document

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