A few results concerning the Hurwitz stability of polytopes of complex polynomials

Let Cf1,…,fm be a polytope generated by complex polynomials f1,…,fm whose degrees differ at most by one. The main goal of this note is to provide a tool for verifying whether a polynomial family Cf1,…,fm is stable. The note extend a few important results of the robust stability theory (the Edge Theorem given by Bartlett et al. (1988) [5], its generalizations proposed by Sideris and Barmish (1989) [7] and Fu and Barmish (1989) [6] and the eigenvalue criterions of Białas (1985, 2004) [4,11]) to more general cases concerning complex polynomial families without degree-invariant assumptions. Numerical examples are presented to complete and illustrate the results.