Lasalle's invariant principle via vector Lyapunov functions of a class of discontinuous systems

It is mainly discussed Lasalle's invariant principle for a class of nonlinear systems with discontinuous righthand sides on the basis of vector Lyapunov function in the framework of Filippov solutions. Assuming that the system is Lebesgue measurable and non-Lipschitz continuous, we extend Lasalle's invariant principle for a class of discontinuous dynamical systems by means of Filippov solutions and vector Lyapunov function which satisfies Lipschitz continuity and regular property.