Terminal sliding mode controller for second order system guaranteeing minimum convergence time

Although most of control methodologies have been focused on the asymptotic stability, the finite time stabilization is more important in the actual industrial applications because the asymptotic stability cannot say anything on the convergence time. For sliding mode controls, terminal sliding mode controllers have been proposed to ensure the finite time convergence. However, there has been no analysis on the condition for the minimum convergence time. Thus, in this paper, we derived a condition of an exponent of a terminal sliding surface which is designed for a second order linear system with no disturbance. Some simulation results are given to show the effectiveness of the result.