Reformulating Phase-Shifting Property in Dynamic Harmonic Domain: Time-Periodic Case

The phase-shifting property has been formulated in the dynamic harmonic domain in a recently published paper. The main idea is to apply a phase-shifting matrix to the output when phase-shifting the inputs by an angle α. This letter demonstrates that the phase-shifting property has to be reformulated when applied to time-periodic systems involving switching functions. The proposed reformulated property assumes proper commutation of the phase-shifting matrix and achieves zero error regardless the periodic system under study.