Stabilization of a planar slow-fast system at a non-hyperbolic point

H. Jardón Kojakhmetov; Jacquelien M.A. Scherpen

Stabilization of a planar slow-fast system at a non-hyperbolic point

Discrete Technology and Production Automation

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Abstract

In this document we study the stabilization problem of a planar slow-fast system at a non-hyperbolic point. At these type of points, the classical theory of singular perturbations is not applicable and new techniques need to be introduced in order to design a controller that stabilizes such a point. We show that using geometric desingularization (also known as blow up), it is possible to design, in a simple way, controllers that stabilize non-hyperbolic equilibrium points of slow-fast systems. Our results are exemplified on the van der Pol oscillator.

Original language	English
Title of host publication	Proceedings of the 22nd International Symposium on the Mathematical Theory of Networks and Systems
Publisher	University of Minnesota Press
Pages	602-607
Number of pages	6
Publication status	Published - Jul-2016
Event	22nd International Symposium on the Mathematical Theory of Networks and Systems - Minneapolis, MN, United States Duration: 12-Jul-2016 → 15-Jul-2016

Conference

Conference	22nd International Symposium on the Mathematical Theory of Networks and Systems
Country/Territory	United States
City	Minneapolis, MN
Period	12/07/2016 → 15/07/2016

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title = "Stabilization of a planar slow-fast system at a non-hyperbolic point",

abstract = "In this document we study the stabilization problem of a planar slow-fast system at a non-hyperbolic point. At these type of points, the classical theory of singular perturbations is not applicable and new techniques need to be introduced in order to design a controller that stabilizes such a point. We show that using geometric desingularization (also known as blow up), it is possible to design, in a simple way, controllers that stabilize non-hyperbolic equilibrium points of slow-fast systems. Our results are exemplified on the van der Pol oscillator.",

author = "\{Jard{\'o}n Kojakhmetov\}, H. and Scherpen, \{Jacquelien M.A.\}",

year = "2016",

month = jul,

language = "English",

pages = "602--607",

booktitle = "Proceedings of the 22nd International Symposium on the Mathematical Theory of Networks and Systems",

publisher = "University of Minnesota Press",

note = "22nd International Symposium on the Mathematical Theory of Networks and Systems ; Conference date: 12-07-2016 Through 15-07-2016",

}

Jardón Kojakhmetov, H & Scherpen, JMA 2016, Stabilization of a planar slow-fast system at a non-hyperbolic point. in Proceedings of the 22nd International Symposium on the Mathematical Theory of Networks and Systems. University of Minnesota Press, pp. 602-607, 22nd International Symposium on the Mathematical Theory of Networks and Systems, Minneapolis, MN, United States, 12/07/2016.

Stabilization of a planar slow-fast system at a non-hyperbolic point. / Jardón Kojakhmetov, H.; Scherpen, Jacquelien M.A.
Proceedings of the 22nd International Symposium on the Mathematical Theory of Networks and Systems. University of Minnesota Press, 2016. p. 602-607.

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

TY - GEN

T1 - Stabilization of a planar slow-fast system at a non-hyperbolic point

AU - Jardón Kojakhmetov, H.

AU - Scherpen, Jacquelien M.A.

PY - 2016/7

Y1 - 2016/7

N2 - In this document we study the stabilization problem of a planar slow-fast system at a non-hyperbolic point. At these type of points, the classical theory of singular perturbations is not applicable and new techniques need to be introduced in order to design a controller that stabilizes such a point. We show that using geometric desingularization (also known as blow up), it is possible to design, in a simple way, controllers that stabilize non-hyperbolic equilibrium points of slow-fast systems. Our results are exemplified on the van der Pol oscillator.

AB - In this document we study the stabilization problem of a planar slow-fast system at a non-hyperbolic point. At these type of points, the classical theory of singular perturbations is not applicable and new techniques need to be introduced in order to design a controller that stabilizes such a point. We show that using geometric desingularization (also known as blow up), it is possible to design, in a simple way, controllers that stabilize non-hyperbolic equilibrium points of slow-fast systems. Our results are exemplified on the van der Pol oscillator.

M3 - Conference contribution

SP - 602

EP - 607

BT - Proceedings of the 22nd International Symposium on the Mathematical Theory of Networks and Systems

PB - University of Minnesota Press

T2 - 22nd International Symposium on the Mathematical Theory of Networks and Systems

Y2 - 12 July 2016 through 15 July 2016

ER -

Stabilization of a planar slow-fast system at a non-hyperbolic point

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