Frequency domain criteria for robust stability of bivariate polynomials

The problem of robust strict-sense Hurwitz stability for bivariate polynomials is considered. A general criterion is formulated as a zero exclusion principle. Attempts are made to construct a value set for a wide class of coefficient perturbations. Interval, disc and linear families for both continuous time and discrete time cases are studied. All conditions for robust stability are written in two-dimensional or one-dimensional frequency domain form. One of examples is a bivariate version of the Nyquist test.<>