Prescribed-time state-feedback stabilization of nonlinear systems with unmatched nonlinear terms

In this paper, we investigate the state-feedback control for nonlinear systems with a prescribed upper bound of the settling time. First, a prescribed-time stability theorem using Lyapunov analysis and a uniformly bounded scaling function is proposed. Then, based on this theorem and the backstepping technique, a finite-time control procedure is provided for the uncertain nonlinear systems with unmatched nonlinear terms. Based on the design procedure, a state-feedback controller is obtained, which can render the system states exactly convergent to zero in a prescribed time and maintain at zero thereafter. Finally, simulation examples are used to demonstrate the effectiveness of the proposed scheme.