Robustness of discrete periodically time-varying control under LTI unstructured perturbations

This note investigates robustness of linear periodically time varying (LPTV) control of discrete linear time invariant (LTI) plants subject to LTI unstructured perturbations. The note first derives a necessary and sufficient condition for robust stability of an LPTV system subject to LTI perturbations, which is less conservative than the well known small gain condition. It then presents a quantitative analysis on the robustness of LPTV control under LTI unstructured perturbations in comparison with that of LTI control. It is shown that under the normal value of the controller period suggested in the previous literature, the stability margin is deteriorated by LPTV control if LTI unstructured perturbations are considered. Hence LTI control is superior to LPTV control in this respect.