For a standard discrete feedback control system, the closed-loop system is stable if the poles of the closed-loop transfer function are all inside the unit circle. The closed-loop transfer function is
so the roots of
must be less than 1 in magnitude.
Consider a first-order process, where the output is temperature (°C), the manipulated input is valve position (%), and the time unit is minutes.
If discretized with a sample time of 1 minute, ...