This correctly shows that the differential equation, \dot V(x1, x2), is asymptotically stable about the origin (refer to the following link).
http://en.wikipedia.org/wiki/Lyapunov_function
By LaSalle's theorem, the closed-loop system is asymptotically stable, and the origin is a finite-time stable equilibrium.
This guarantees finite time stability (using negative homogeneity) for double integrator system.
End of Proof.
(2) The paper [BB97] is a good reference for the proof.
[BB97] S.P. Bhat and D.S. Bernstein, "Finite-Time Stability of Homogeneous Systems," Proceedings of IEEE ACC, Albuquerque, New Mexico, June 1997, pp. 2513-2514.
(3) Recent discussions on control system design approaches can be found in the following RG link.
"What are trends in control theory and its applications in physical systems (from a research point of view)?"