A321 First Officer reported descending to a lower altitude after experiencing a cabin pressure loss at FL310. Pressurization control was re-established after descent; and the flight continued to destination.

Narrative

It was the first leg of a two day trip. We departed with no issues. While at cruise at FL310 we experienced a rapid decompression. We received four different ECAM messages all revolving around the cabin pressure. At one point the cabin altitude had reached 24K. As pilot flying I immediately said my aircraft and after the Captain [requested assistance] and asked for 10k feet I immediately started the [priority handling] descent. The Captain completed the [priority handling] descent checklist on the QRC followed by the ECAM actions. Once leveled at 10K feet cabin pressure controller 1 appeared to be functioning properly and the cabin pressurization system began to stabilize. The Captain decided to continue on to ZZZ at 10K feet and we landed without further issues. Once at the gate in ZZZ Maintenance was notified and the Captain made all the appropriate write ups in the logbook. Both me and the Captain were met by the ZZZ Chief Pilot and a Check Pilot just asking for a quick debrief and wanted to know if we felt safe to continue flying the remainder of the trip. Both me and the Captain agreed we were safe to continue flying. Cause: I really can't think of anything we could have done different. I think we both did a great job working together to get the situation under control. The Captain did a good job of communicating with the passengers; flight attendants and Dispatch.