Construction of nonpathological Lyapunov functions for discontinuous systems with Caratheodory solutions

2010 ◽  
Vol 14 (1) ◽  
pp. 284-287 ◽  
Author(s):  
Alireza Faraji Armaki ◽  
Naser Pariz ◽  
Rajab Asgharian
Keyword(s):  
Lyapunov Functions ◽  
Discontinuous Systems ◽  
Carathéodory Solutions

On stability of discontinuous systems via vector Lyapunov functions

2007 ◽  
Vol 28 (12) ◽  
pp. 1613-1619 ◽  
Author(s):  
Xiao-wu Mu ◽  
Gui-fang Cheng ◽  
Zhi-shuai Ding
Keyword(s):  
Lyapunov Functions ◽  
Discontinuous Systems ◽  
Vector Lyapunov Functions

scholarly journals Lyapunov stability for discontinuous systems

2020 ◽  
Vol 42 ◽  
pp. e17
Author(s):  
Iguer Santos
Keyword(s):  
Stability Analysis ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Lyapunov Stability ◽  
Lyapunov Functions ◽  
Discontinuous Systems ◽  
Discontinuous Differential Equations ◽  
Nonautonomous Differential Equations ◽  
The Stability ◽  
Lyapunov Sense

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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