An analysis was made of robust stability by estimating the robust confidence region for the roots of the characteristic Equation of a process, which uses a typical PID controller with auto-tuning. From standard statistical concepts, considerations on the statistical distance associated with the chi-square distribution were taken into account when establishing the methodology, which enabled the region of robust stability to be found. The results show the robust stability region for all eigenvalues of characteristic equation, thus demonstrating the ability of the procedure. The region of stability can be updated online, thus enabling the stability of the system to be continuously evaluated, with little computational effort.