It is well known that an nth-order real polynomial D(z)= is Schur stable if its coefficients satisfy the monotonic condition, i.e., dn > dn-1 > > d1 > d0 > 0. In this letter it is shown that even if the monotonic condition is violated by one coefficient (say dk), D(z) is still Schur stable if the deviation of dk from dk+1 or dk-1 is not too large. More precisely we derive upper bounds for the admissible deviations of dk from dk+1 or dk-1 to ensure the Schur stability of D(z). It is also shown that the results obtained in this letter always yield the larger stability range for dk than an existing result.

In this letter a simplified Jury's table for real polynomials is extended to complex polynomials. Then it is shown that the extended table contains information on the root distribution of complex polynomials with respect to the unit circle in the complex plane. The result given in this letter is distinct from the recent one in that root counting is performed in a different way.

Recently a simple proof of Jury test for complex polynomials was given by the author. In this letter further extended results are presented. Another elementary proof of the Schur stability condition is provided. More importantly it is shown that the stability table can also be used to determine the root distribution of complex polynomials with respect to the unit circle in the complex plane.

Recently some attempts have been made in the literature to give simple proofs of Jury test for real polynomials. This letter presents a similar result for complex polynomials. A simple proof of Jury test for complex polynomials is provided based on the Rouche's Theorem and a single-parameter characterization of Schur stability property for complex polynomials.

This letter concerns the Schur stability of convex combinations of complex polynomials. For given two Schur stable complex polynomials, a sufficient condition is given such that the convex combination of polynomials is also Schur stable.

Monotonic condition, a well-known sufficient condition for Schur stability of real polynomials, is relaxed. The condition reads that a series of strictly and monotonically decreasing positive coefficients of the polynomials yields Schur stability. It is shown by inspecting the original proof that equalities are allowed in all the inequalities but two which are located at appropriate positions.

For a real Schur polynomial, estimates are derived for a Schur stability margin in terms of matrix entries or tableau entries in some stability test methods. An average size of the zeros of the polynomial is also estimated. These estimates enable us to obtain more information than stability once a polynomial is tested to be stable via the established Schur stability criterion for real polynomials.

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.