ABSTRACT
The stability is a structural systemic property directly related to the type of system response. The response may be bounded or asymptotically tend to zero. Otherwise, the system response would take emphatically high values, which would remove the system by its modeling limits or cause damage to the system itself. If the system characteristic equation has roots in the circumference of the unit cycle with all other roots being located inside, then the steady-state output will operate unabated oscillations of finite amplitude when its input is a finite function. The output of a stable system is within acceptable limits while the corresponding output of an unstable system theoretically tends to infinity. The most prevalent techniques for determining the stability of a discrete-time system are: unit-circle criterion; Routh criterion using the bilinear mobius transformation; Jury criterion; Root locus method; Nyquist stability criterion; and Bode stability criterion.
