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An Extension of Lyapunov’s First Method to Nonlinear Systems With Non-Continuously Differentiable Vector Fields

Hugo Lhachemi, David Saussié and Guchuan Zhu

Article (2017)

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Cite this document: Lhachemi, H., Saussié, D. & Zhu, G. (2017). An Extension of Lyapunov’s First Method to Nonlinear Systems With Non-Continuously Differentiable Vector Fields. IEEE Control Systems Letters, 1(1), p. 74-79. doi:10.1109/lcsys.2017.2705096
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Abstract

This letter investigates the extension of Lyapunov's first method to nonlinear systems in the case where the C1-regularity assumption, i.e., the underlying vector field is continuously differentiable, is not satisfied. It is shown that if this regularity assumption is not fulfilled, the Hurwitz nature of the Jacobian matrix, if it exists, does not guarantee the stability of the original nonlinear system. Under weaker assumptions than the C1-regularity, namely the existence of the directional derivatives of the vector field, conditions for guaranteeing the local exponential stability of the nonlinear system are derived.

Uncontrolled Keywords

Lyapunov methods,stability of nonlinear systems

Open Access document in PolyPublie
Subjects: 2500 Génie électrique et électronique > 2500 Génie électrique et électronique
Department: Département de génie électrique
Research Center: Non applicable
Date Deposited: 21 Dec 2017 15:20
Last Modified: 24 Oct 2018 16:12
PolyPublie URL: https://publications.polymtl.ca/2844/
Document issued by the official publisher
Journal Title: IEEE Control Systems Letters (vol. 1, no. 1)
Publisher: IEEE
Official URL: https://doi.org/10.1109/lcsys.2017.2705096

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