Cessna Citation 525 pilot reported the cabin pressurization controller malfunctioned during arrival. The flight crew continued to the destination airport and the aircraft was subsequently sent for maintenance.

Narrative

Our flight this day was from ZZZ1 to ZZZ. It was non eventful until we started our descent. We were given the ZZZZZ1 RNAV arrival and assigned to descend via the arrival. As the aircraft started down; I pulled the throttles back to idle so as to not overspeed. As I was bringing them back; I felt my ears pop and I looked at the pressurization controller. It was set as appropriate to our landing field height; but the rate was climbing at 1900 fpm. I pointed it out to my copilot and asked him to tell ATC that we needed to keep going down. Moments later; we got the CABIN ALT annunciator. At that point; we completed the memory items; informed ATC that we were continuing our descent due to a cabin pressurization issue. On the descent; the pressurization controller rate would vary from +1900fpm to -300fpm; but it never stabilized. We were cleared down to 13000 ft. We observed the cabin altitude indicate approximately 14000 ft; but no higher. At no point did the O2 masks for the passengers deploy automatically; nor did we manually drop them since we were expediting down and never completely depressurized. We continued our flight to ZZZ and the pressurization controller continued to act erratically. We landed safely in ZZZ with no further issues. The airplane was repositioned to ZZZ2 for service at the Textron Maintenance facility. We have yet to hear of their findings.