Fundamental limitations in self-sensing magnetic bearings when modeled as linear periodic systems

In "Magnetic bearing measurement configurations and associated robustness and performance limitations", Thibeault and Smith demonstrate that self-sensing magnetic bearings are impractical due to fundamental limitations in the achievable closed-loop robustness. Due to experimental data which appeared to contradict these results, Maslen, Montie, and Iwasaki showed that significantly better robustness is achievable in "Robustness limitations in self-sensing magnetic bearings" if the magnetic bearing is modeled as a linear periodic (LP) system rather than the linear time invariant (LTI) system used by Thibeault and Smith. The present paper explores why modeling the self-sensing magnetic bearing as a LP system improves the achievable robustness. This is accomplished by utilizing lifting to analyze the LP model as a MIMO discrete LTI system