Department of Mathematics, Faculty of Science, Anadolu University, 26470 Eskisehir, Turkey
Copyright © 2010 Handan Akyar et al. This is an open access article distributed under the
Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
The Schur and Hurwitz stability problems for a parametric polynomial
family as well as the Schur stability problem for a compact set of real
matrix family are considered. It is established that the Schur stability
of a family of real matrices is equivalent to the nonsingularity
of the family if has at
least one stable member. Based on the Bernstein expansion of a
multivariable polynomial and extremal properties of a multilinear
function, fast algorithms are suggested.