Multivariable Nyquist theory
Raymond A. DeCarlo, J. Murray, Richard E. Saeks · International Journal of Control · 1977
It is shown that a multivariable digital filter is stable if and only if A(z1, z2…,zn)≠0 when | z1 1| = | z2|=… = |zn| = 1 and the Nyquist plot for the single-variable function A(z, z, … z) does not encircle zero. Here A(z1, z2… zn) is the denominator polynomial of the relatively prime rational transfer function of the digital filter.