Nonsingular terminal sliding surface with rational exponent

In many of applications, the finite time stabilization is very important. However, most of control schemes proposed so far have been focused on the verification of asymptotic stability. To get a finite time convergence property, terminal sliding mode control schemes have been proposed. However, they suffer from singularity problem. Thus, in this paper, we propose a nonsingular terminal sliding surface. The proposed method guarantees that it won´t suffer from singularity. In addition, the exponent of a power function in the sliding surface can be a ration number although it should be a rational number with odd numerator and denominator in the conventional method.