Time-Synchronized Control for Disturbed Systems

Finite-time control is concerned with steering a system state to the origin before a certain settling-time limit, ignoring any consideration of when each state element converges relative to the others. In this article, a control problem called time-synchronized control is investigated, where all the system state elements have to converge to the origin at the same time. To facilitate this problem formulation, we introduce the notion of time-synchronized stability together with sufficient Lyapunov conditions. Based on these, the analytical solution of a time-synchronized stable system is obtained and discussed, explicitly offering a quantitative method to preview and predesign the control system performance in prior. Following these results, a robust time-synchronized control law is designed for multivariable systems under external disturbances and model uncertainties. Finally, comparative numerical simulations between time-synchronized control and finite/fixed/prescribed-time control are conducted to showcase the time-synchronized features attained.