Properties of isostables and basins of attraction of monotone systems

Aivar Sootla, Alexandre Mauroy

Research output: Contribution in Book/Catalog/Report/Conference proceedingConference contribution

Abstract

In this paper, we investigate geometric properties of monotone systems by studying their isostables and basins of attraction. Isostables are boundaries of specific forward-invariant sets defined by the so-called Koopman operator, which provides a linear infinite-dimensional description of a nonlinear system. First, we study the spectral properties of the Koopman operator and the associated semigroup in the context of monotone systems. Our results generalize the celebrated Perron-Frobenius theorem to the nonlinear case and allow us to derive geometric properties of isostables and basins of attraction. Additionally, we show that under certain conditions we can characterize the bounds on the basins of attraction under parametric uncertainty in the vector field. We discuss computational approaches to estimate isostables and basins of attraction and illustrate the results on two and four state monotone systems.

Original languageEnglish
Title of host publication2016 American Control Conference, ACC 2016
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages7365-7370
Number of pages6
Volume2016-July
ISBN (Electronic)9781467386821
DOIs
Publication statusPublished - 28 Jul 2016
Externally publishedYes
Event2016 American Control Conference, ACC 2016 - Boston, United States
Duration: 6 Jul 20168 Jul 2016

Conference

Conference2016 American Control Conference, ACC 2016
CountryUnited States
CityBoston
Period6/07/168/07/16

Fingerprint

Nonlinear systems
Uncertainty

Keywords

  • Basins of attraction
  • Isostables
  • Koopman operator
  • Monotone systems
  • Nonlinear Perron-Frobenius theorem

Cite this

Sootla, A., & Mauroy, A. (2016). Properties of isostables and basins of attraction of monotone systems. In 2016 American Control Conference, ACC 2016 (Vol. 2016-July, pp. 7365-7370). [7526835] Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/ACC.2016.7526835
Sootla, Aivar ; Mauroy, Alexandre. / Properties of isostables and basins of attraction of monotone systems. 2016 American Control Conference, ACC 2016. Vol. 2016-July Institute of Electrical and Electronics Engineers Inc., 2016. pp. 7365-7370
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Sootla, A & Mauroy, A 2016, Properties of isostables and basins of attraction of monotone systems. in 2016 American Control Conference, ACC 2016. vol. 2016-July, 7526835, Institute of Electrical and Electronics Engineers Inc., pp. 7365-7370, 2016 American Control Conference, ACC 2016, Boston, United States, 6/07/16. https://doi.org/10.1109/ACC.2016.7526835

Properties of isostables and basins of attraction of monotone systems. / Sootla, Aivar; Mauroy, Alexandre.

2016 American Control Conference, ACC 2016. Vol. 2016-July Institute of Electrical and Electronics Engineers Inc., 2016. p. 7365-7370 7526835.

Research output: Contribution in Book/Catalog/Report/Conference proceedingConference contribution

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Sootla A, Mauroy A. Properties of isostables and basins of attraction of monotone systems. In 2016 American Control Conference, ACC 2016. Vol. 2016-July. Institute of Electrical and Electronics Engineers Inc. 2016. p. 7365-7370. 7526835 https://doi.org/10.1109/ACC.2016.7526835