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

Hugo Lhachemi, David Saussié, Guchuan Zhu

Article (2017)

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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

Subjects: 2500 Electrical and electronic engineering > 2500 Electrical and electronic engineering
Department: Department of Electrical Engineering
PolyPublie URL: https://publications.polymtl.ca/2844/
Journal Title: IEEE Control Systems Letters (vol. 1, no. 1)
Publisher: IEEE
DOI: 10.1109/lcsys.2017.2705096
Official URL: https://doi.org/10.1109/lcsys.2017.2705096
Date Deposited: 21 Dec 2017 15:20
Last Modified: 26 Nov 2022 18:16
Cite in APA 7: 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), 74-79. https://doi.org/10.1109/lcsys.2017.2705096

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