Lyapunov stability for discontinuous systems

Authors

DOI:

https://doi.org/10.5902/2179460X42344

Abstract

The present work studies the stability analysis of equilibrium of ordinary differential equations with the discontinuous right side, also called discontinuous differential equations, using the notion of Carathéodory solution for differential equations. This way, it is studied the stability of equilibrium in the Lyapunov sense for discontinuous systems through nonsmooth Lyapunov functions. Then two existing Lyapunov theorems are obtained. The results established refer to systems determined by nonautonomous differential equations.

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Author Biography

Iguer Santos, Unesp - São Paulo State University

Iguer Luis Domini dos Santos has a degree in
Mathematics (2005), a Master in Mathematics (2008)
and a doctorate in Mathematics (2011) from Sao Paulo
State University. He is currently an assistant professor
in the department of mathematics at the Sao Paulo
State University.

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Published

2020-05-15

How to Cite

Santos, I. (2020). Lyapunov stability for discontinuous systems. Ciência E Natura, 42, e17. https://doi.org/10.5902/2179460X42344