Consider the system
where is continuous, is the set of all solutions of system (1). The origin is weakly finite time stable for system (1) if the origin is Lyapunov stable for system (1) and for all there exists such that if then for all is defined for and there exists such that for all is called the setting time of the solution If then the origin is finite time stable for system (1). One of the theorems is based on a Lyapunov function such that
for all where is a continuous definite function,
Theorem. Let the origin be an equilibrium point for system (1). If there exists a continuously differentiable Lyapunov function satisfying condition (2) such that for some
then the origin (1) is finite time stable for system (1).