This paper proposes a novel formulation for robust predefined-time stabilisation of a class of second-order systems with matched perturbations. The presented approach allows designing a family of controllers that enforce a predefined-time sliding motion, even in the presence of unknown but bounded perturbations, such that, during the sliding motion, the state slides to the origin in predefined-time. Consequently, the origin of the closed-loop system is globally predefined-time stable. The analysis and design of the proposed controllers rely on the Lyapunov framework and a novel class of nonlinear functions, providing stability and robustness conditions for the closed-loop system. Finally, numerical simulations are conducted to highlight the reliability of the proposed scheme.

本文提出了一种新颖的公式，用于对一类具有匹配摄动的二阶系统进行鲁棒的预定义时间稳定。提出的方法允许设计一系列控制器，即使在存在未知但有界扰动的情况下，也可以强制执行预定时间的滑动运动，从而在滑动运动期间，状态会在预定时间滑动至原点。因此，闭环系统的起源是全局预定义的时间稳定的。所提出的控制器的分析和设计依赖于Lyapunov框架和一类新型的非线性函数，为闭环系统提供了稳定性和鲁棒性条件。最后，进行数值模拟以突出所提出方案的可靠性。