In this letter we present some easily checkable necessary conditions for a polynomial with positive coefficients to have all its zeros in a prescribed sector in the left half of the complex plane. As an auxiliary result, we also obtain a new necessary condition for the Hurwitz stability.

This letter addresses stability problems of interval matrices stemming from robustness issues in control theory. A quick overview is first made pertaining to methods to obtain stability conditions of interval matrices, putting particular emphasis upon one of them, regularity condition approach. Then, making use of this approach, several new stability criteria, for both Hurwitz and Schur stability, are derived.

It is shown that for a class of interval matrices we can estimate the location of eigenvalues in a very simple way. This class is characterized by the property that eigenvalues of any real linear combination of member matrices are all real and thus includes symmetric interval matrices as a subclass. Upper and lower bounds for each eigenvalue of such a class of interval matrices are provided. This enables us to obtain Hurwitz stability conditions and Schur ones for the class of interval matrices and positive definiteness conditions for symmetric interval matrices.