A Time-Synchronized Convergence Property

In consideration of unique finite-time stability, a control problem is introduced in this paper, where exactly at the same time, all system state elements reach zero. To articulate this problem, time-synchronized stability (TSS) is suitably defined by a sufficient Lyapunov-type condition. According to the formulation of TSS, two distinctive sign functions are revisited. It is found that both sign functions can be used in control design to stabilize a system, while the controller based on a specific sign function called the norm-normalized one additionally contributes to the achievement of TSS. Further, comparative studies are conducted to showcase the full strength of the proposed algorithms.