CL-350 fractional jet Captain reported an engine malfunction on the final descent and following checklists shut down the engine. The flight landed at the destination without incident.

Narrative

Flying one pax from ZZZ1 to ZZZ. My flying partner and I had just requested deviations around some convective weather on the ZZZZZ X arrival for ZZZ. On the final descent and transition to the approach phase of flight; we recognized engine vibration and isolated the vibration to the RH ENGINE. Moments later; R ENGINE VIBRATION AMBER CAS illuminated. We ran QRH for said CAS and elected to remain monitoring the vibration. After a few minutes; we noticed the RH Interstage Turbine Temperature (ITT) rising towards redline and subsequent R ENGINE EXCEEDANCE CAS became intermittent. In the interest of safety and any further damage; we ran the INFLIGHT ENGINE SHUTDOWN QRC and subsequent checklists and landed without incident. My flying partner gave a brief statement to the airport operations supervisor at ZZZ. I debriefed our one passenger on what happened and listened to him share some previous experiences over his years as a company shareholder. We got him on his way and my partner and I debriefed the incident and made appropriate phone calls. After visual inspection; crew noticed no visible abnormalities in the fan duct and/or the exhaust duct.Suggestions: My second in command (SIC) and I feel relatively comfortable with our actions and results due to compliance with SOP's and checklists. Obviously shutting an engine down in flight is never comfortable; but it was necessary.