Time Base Generator-Based Practical Predefined-Time Stabilization of High-Order Systems With Unknown Disturbance

This brief investigates a predefined-time stabilization problem for a high-order integrator chain system with an unknown disturbance by using a time base generator (TBG) method. Until now it is still a challenge to realize the TBG based predefined-time stabilization for high-order systems. In this brief, a novel TBG function is constructed for a high-order integrator system and a nonlinear coordinate transformation is proposed to facilitate the design of the predefined-time controller. The feature of this TBG function is that it is smooth and applicable to arbitrary order systems. Then the practical predefined-time stability of the closed-loop system is analyzed under the proposed TBG based controller when an unknown disturbance exists in the system. Furthermore, the settling time can be preset arbitrarily, and thus is independent of the system's initial condition. Finally, some numerical examples are presented to validate the effectiveness of the proposed TBG based control strategy.