A220 flight crew reported rudder control system failure in flight. Flight crew continued to destination airport and completed an uneventful landing.

Narrative

During cruise at FL360 shortly before starting descent; I observed a 'FLIGHT CONTROL FAULT' ECAM message which immediately went away. After starting our descent I noticed the message come back two more times and disappear. At approximately FL270 the message returned and stayed illuminated. Shortly after a Red 'RUDDER FAIL' message displayed along with master caution and chime. I was Pilot Flying (PF) and after discussing the aircraft flight path with the First Officer (FO); I stated that I would transfer control of the aircraft and the radios to him in order to assess the situation. After ensuring a stable flight path and a plan to continue towards ZZZ I transferred control and ran the Emergency Checklist. The rudder had failed in the center position and the Emergency Checklist directed us to land immediately. As the runway at ZZZ was suitable we elected to continue to ZZZ and as this was a RED ECAM item and a primary flight control we elected to [request priority handling]. I informed the Flight Attendants that this would be a priority situation and that an evacuation was not planned and the time to touchdown. I finished the remainder of the Emergency Checklist that was deferred to approach and set up for the RNAV RNP XXL in ZZZ. After briefing the approach I took control of the aircraft back. We landed in ZZZ uneventfully and taxied to the gate. We had no issues taxing with full nose wheel steering. After parking and deplaning a logbook discrepancy was entered.