Terminal sliding mode control of second-order systems with bounded input

There are many results on terminal sliding mode control of nonlinear systems in the literature. Nevertheless, none of them are concerned about systems with bounded input. To this end, a new approach is proposed to solve the terminal sliding mode control of systems with bounded input. The control design can be divided into two steps. The first step is to design a novel terminal sliding mode manifold by combining the non-singular terminal sliding mode manifold and a kind of saturation function. The second step is to design a saturated controller for the considered second-order nonlinear system such that the states will reach and be kept on the designed sliding mode manifold. Based on the above steps, the states will first reach the sliding mode and then slide to the origin in finite time along the sliding mode manifold.