Cessna Citation V pilot reported two aircraft stalls due to icing conditions while descending for an approach. The pilot recovered the aircraft and landed.

Narrative

On Day 0 I piloted a flight from ZZZ to ZZZ1. My wife was sitting in the front facing seat of the club configuration in the back of the airplane and luckily; she was wearing both her lap and shoulder belts since she knew it was going to be a short flight. The flight started at XA:53:00 p.m. I had filed for an altitude of 13;000'; but as I proceeded eastbound; I saw a cloud layer a bit above my altitude; so I requested 15;000' which center granted me. At approximately XB:09; I was cleared down to 13;000' and then to 11;000' and was still clear of clouds.It was obvious that I was going to be entering clouds going below 11;000'; so I turned on the engine anti-ice. The white lights came on the panel showing that the required temperature of the anti-ice was not yet attained; and a few minutes later the light extinguished; confirming the engines were now protected from ice. As I entered the clouds for the descent; everything seemed normal; so I pulled back the speed to 150 kts. I asked for vectors to join the approach; and I activated my GPS for the ILS XX at ZZZ1. The controller said to maintain 9;000' until established at ZZZZZ. It was shortly after that communication that the airplane entered a violent stall to the right; but there was no stall warning signal or any buffet before. I corrected with aileron and rudder; not realizing what was happening and as the airplane corrected to the left; it entered a violent stall to the left. This time I heard a faint signal of the stall warning; so I glanced at the airspeed and it was 145 knots. Right away I applied max power and lowered the nose. The airspeed went to 245 kts. I was fighting hard to recover control of the airplane; but I did come out of the cloud shortly after. I still was not sure what was happening.I did advice ATC at that point; although I realized as I was saying it that there was actually very little the controller could do to help out. He suggested that I maintain VFR after I told him I was out of the cloud; which I did. I did actuate the boots a few times when I realized that I had picked up a fair bit of ice on the wings. I did see some ice come off the wing after that; but I was not sure how much ice was on the wing. I continued the approach after I regained control of the aircraft and completed the landing uneventfully. It was only after I exited the aircraft that I saw a lot of clear ice still attached to the wing. I tried to break it off with my hand; but it was so hard I could not break it. Unfortunately; I did not think of taking a picture of the wing and the airplane at that time. I have had a lot of experience flying a Cessna 414A in the northeast from XXXX to XXXX; but it was mostly 'rime' ice that I recalled. I also experienced some icing with my TBM700 from XXXX to XXXX; but this was really my first encounter with significant clear icing in this airplane. I know that every airplane behaves differently in icing; but I admit now that I felt my jet would be less affected by icing. I just don't believe this is the case anymore. I hope other pilots of Citation V and similar aircraft can learn from my experience; so I think it's important that I understand as much as possible what happened.