Extending Kharitonov's theorem to eigenvalues clustering in subregions of the complex plane

Sufficient conditions are developed for root clustering of a polynomial in a transformable region when each of the polynomial coefficients takes an arbitrary but fixed value within a specified closed interval. The conditions are in terms of the Kronecker products or the bialternate products. The sufficient conditions are then applied to different subregions in the complex plane. The work of Barmish (1984) on the invariance of the strict Hurwitz property for interval polynomials with perturbed coefficients is extended to root clustering in a region.