Lyapunov Instability for Discontinuous Differential Equations

O presente trabalho estuda a instabilidade de Lyapunov para equações diferenciais descontínuas através do uso da noção de solução de Carathéodory para equações diferenciais. A partir do primeiro teorema de instabilidade de Lyapunov e do teorema de instabilidade de Chetaev, que tratam da instabilidade para equações diferenciais ordinárias, dois resultados de instabilidade de Lyapunov para equações diferenciais descontínuas são obtidos.The present work studies the Lyapunov instability for discontinuous differential equations through the use of the notion of Carathéodory solution to differential equations. From Lyapunov's first instability theorem and Chetaev's instability theorem, which deal with instability to ordinary differential equations, two Lyapunov instability results for discontinuous differential equations are obtained

Lyapunov stability for discontinuous systems

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