Backstepping-Induced Terminal Sliding Mode Control with Strict Lyapunov Function

In this paper a different view on the classical Terminal Sliding Mode (TSM) control is presented. The backstepping procedure is used to synthesize a new TSM-like control law for the second and third order integrator chain. A strict Lyapunov function (LF) for the entire closed loop dynamics is given naturally by design. Further, it is shown, under a certain choice of parameters, that the LF is valid for the classical TSM control law, as well. Finite-time convergence of all states to the origin is proven for both control algorithms using this LF. Finally, the new TSM-like control law is validated in simulations for the third order case.