Prescribed‐time stabilization ofp‐normal nonlinear systems by bounded time‐varying feedback

Abstract This article studies the prescribed‐time stabilization problem of p ‐normal nonlinear systems by bounded time‐varying high‐gain feedback. A time‐varying bounded controller, which can achieve prescribed‐time stabilization, is designed via backstepping. Because of the usage of time‐varying high‐gain functions which grow unbounded as the time tends to the prescribed time, the usual separation technique is invalid. To solve this problem, a novel design scheme is proposed. It is shown that all of the closed‐loop trajectories convergence to the origin in prescribed time. Finally, a numerical example verifies the effectiveness of the proposed method.