Non-singular terminal sliding mode controller design for nonlinear systems with prescribed convergence time guarantees

This paper considers the prescribed-time non-singular terminal sliding mode control (TSMC) for nonlinear systems with uncertainties bounded by non-negative functions. At first, a new Lyapunov theorem for prescribed-time stability is introduced. Then, a novel terminal sliding surface together with a non-singular TSMC input is constructed by using a time-varying scaling function. Strict analysis shows that the proposed controller is able to ensure the exact reaching of the sliding surface as well as the system states to zero in a prescribed time independent of the system initial conditions. Moreover, all the state signals and the control input remain uniformly bounded. Finally, simulation comparison with the existing fixed- and prescribed-time TSMC is given to verify the effectiveness of the theoretical results.