Network realizability theory approach to stability of complex polynomials

In this letter, we briefly point out that concepts in network realizability theory provide the basis for a unified approach to stability (or, in general, root distribution) of a polynomial with complex coefficients. Very recent results in the area, then, become easily interpretable. The same approach can be exploited to prove stability results for interval complex polynomials. The counterpart of the basic continuous system result is stated for discrete systems, where a complex polynomial is to be checked for absence of roots on or outside the unit circle. The suggested procedure has capabilities for generalization to the multivariate case. Among other advantages, savings in the computational complexity in the implementation of stability tests on multidimensional filters emerge.