Variable Step Time Delay Control

This paper presents Variable-step Time Delay Control (VTDC), a proactive aperiodic robust control framework that jointly addresses feedback control and control-update scheduling, rather than treating the controller and triggering mechanism as separate components. Inspired by adaptive stepsize regulation in Runge-Kutta integration, VTDC exploits the fact that the local control error can be structured to scale with the realized timestep. Using sliding-manifold-based Time Delay Control, the resulting System Time Delay Error (TDE), which reflects local model and uncertainty variations, is shown to be quadratically bounded by the control interval. This relation enables a closed-form feedback law that automatically enlarges or reduces the subsequent interval to regulate the TDE magnitude. Because the scheduling law is constructed directly from the controller structure, the next update time is determined algebraically without continuous trigger monitoring, future-state prediction, or iterative search. The resulting variable-step closed loop is shown to admit bounded timesteps and step ratios, exclude Zeno behavior, and render the sliding variable uniformly ultimately bounded. Spacecraft attitude-control simulations further demonstrate the practical feasibility and low computational burden of the proposed framework.