Semi-global stabilization of linear time-varying systems with input saturation and unbounded distributed input delays

This work studies the semi-global stabilization problem for linear time-varying (LTV) systems with both input saturation and unbounded distributed input delays. Based on the parametric differential Riccati equation (DRE), a truncated predictor feedback controller is first developed through the low-gain method. A key property of the control input’s peak magnitude is then established; specifically, it is shown that the peak magnitude can be made arbitrarily small by tuning the parameter in the parametric DRE. It is demonstrated that the truncated predictor feedback controller effectively solves the concerned semi-global stabilization problem. Furthermore, by employing a perturbation theorem for unbounded-delayed systems, the obtained semi-global stabilization results eliminate an implicit assumption on initial conditions that was required in existing works. Finally, the effectiveness and advantages of the proposed control strategy are verified via two numerical simulation examples. © The Author(s), under exclusive licence to Springer Nature B.V. 2026.