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Numerical Design of Lyapunov Functions for a Class of Homogeneous Discontinuous Systems

Abstract : This paper deals with the analytic and numeric design of a Lyapunov function for homogeneous and discontinuous systems. First, the presented converse theorems provide two analytic expressions of homogeneous and locally Lipschitz continuous Lyapunov functions for homogeneous discontinuous systems of negative homogeneity degree, generalizing classical results. Second, a methodology for the numerical construction of those Lyapunov functions is extended to the class of systems under consideration. Finally, the developed theory is applied to the numerical design of a Lyapunov function for some Higher-Order Sliding Mode algorithms.
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https://hal.inria.fr/hal-03140866
Contributor : Denis Efimov Connect in order to contact the contributor
Submitted on : Sunday, February 14, 2021 - 11:33:38 AM
Last modification on : Friday, January 21, 2022 - 3:12:41 AM
Long-term archiving on: : Saturday, May 15, 2021 - 6:05:53 PM

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Jesús Mendoza-Avila, Denis Efimov, Rosane Ushirobira, Jaime Alberto Moreno Pérez. Numerical Design of Lyapunov Functions for a Class of Homogeneous Discontinuous Systems. International Journal of Robust and Nonlinear Control, Wiley, In press, ⟨10.1002/rnc.5478⟩. ⟨hal-03140866⟩

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