PA-34-200 Seneca I
Air Traffic Control Fully Certified
Situational Awareness; Communication Breakdown
Deviation - Altitude Excursion From Assigned Altitude; Inflight Event / Encounter Weather / Turbulence; Inflight Event / Encounter CFTT / CFIT
Air Traffic Control Issued New Clearance
Human Factors; Weather
Aircraft X was IFR from ZZZ. The aircraft had just passed the ZZZ1 airport when I noticed that the aircraft had descended from its initial altitude of 4000 ft. to 3600 ft. and had continued to descend to 3400 ft. I issued a low altitude alert to the aircraft and advised that the aircraft climb to 4000 ft. The pilot then told me that he was heading back to ZZZ. I asked the pilot for the reason for the change in destination and he told me that he was icing up and he did not want to climb back into the clouds where he picked up ice. The aircraft continued to fluctuate in altitude. I advised him that my minimum safe altitude was 3700 ft. The aircraft eventually leveled off at 4000 ft. and went back to ZZZ.
Memphis Center Controller reported an aircraft that descended below the Minimum Safe Altitude due to icing.