The principle of sliding mode control is to force the system to reach a given surface called the sliding surface and to remain there until it reaches equilibrium. This command is done in two steps: the convergence towards the surface, then the sliding the along the path of the desired state. In other words, convergence in finite time is a first step. Finally, asymptotic convergence is the follow-up of the state trajectory of the system.
For more details and information about this subject i suggest you to take a look at links on topic.
-Analysis of finite-time convergence by the method of Lyapunov ...