Practical Explicit-time Stabilization of a Proportional Control System

Proportional control can be realized directly through the amplification of analog signals, and it also has the advantage of easy tuning parameters in digital signal control. However, it is difficult for the proportional control to preset the upper bound of settling time. To address this problem, a novel practical explicit-time control method is proposed. In bounded initial condition, this method makes this system error converge to a predefined neighborhood of zero within an explicit time. More specifically, the initial condition set and conditionally stable set are solved by practical explicit-time stabilization theorem. Based on that, a proportional feedback control is founded to achieve practical conditional fixed-time stability.