On switching manifold design for terminal sliding mode control

In this paper, a general design scheme is proposed for finite-time switching mode manifolds and corresponding nonsingular controllers. The reduced system is obtained from terminal sliding mode control (TSMC) and its homogeneity is investigated, which also illustrates that TSMC is finite-time control by the homogeneous theory. Based on the homogeneity analysis, a design proposal is provided for general finite-time switching manifolds and corresponding controllers, which guarantee that all states of a controlled system are finite-time convergent to the origin. In simulations, three finite-time switching manifolds are presented and the corresponding controllers are validated to perform the finite-time control for the double integral system.