Editing Digital control (section)

=== Stability ===
Although a controller may be stable when implemented as an analog controller, it could be unstable when implemented as a digital controller due to a large sampling interval. During sampling the aliasing modifies the cutoff parameters. Thus the sample rate characterizes the transient response and stability of the compensated system, and must update the values at the controller input often enough so as to not cause instability.

When substituting the frequency into the z operator, regular stability criteria still apply to discrete control systems. [[Nyquist stability criterion|Nyquist criteria]] apply to z-domain transfer functions as well as being general for complex valued functions. Bode stability criteria apply similarly.
[[Jury stability criterion|Jury criterion]] determines the discrete system stability about its characteristic polynomial.