Terminal Sliding Mode Control of the Delayed System by Adopting Derivate Estimator

The paper proposes a terminal sliding mode control for the delayed input system with matched uncertainties. Through the state transformation, the delayed input system with uncertainties is transformed into the non-delayed controllable canonical form For the controllable canonical form, the paper designs a terminal sliding mode and terminal sliding control law with the Lyapunov method that makes both the reaching time of the any initial state and the converging time to the equilibrium points is in finite time. During the designation of the terminal sliding mode, a derivate estimator is adopted. The simulation results show the validation of the method.