International Journal of Mathematics and Mathematical Sciences
Volume 2003 (2003), Issue 2, Pages 75-85
Matrix measure and application to stability of matrices and interval dynamical systems
Department of Basic Sciences, College of Arts and Sciences, University of Sharjah, P.O. 27272, Sharjah, United Arab Emirates
Received 27 February 2002
Copyright © 2003 Ziad Zahreddine. 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.
Using some properties of the matrix measure, we obtain a general
condition for the stability of a convex hull of matrices that
will be applied to study the stability of interval dynamical
systems. Some classical results from stability theory are
reproduced and extended. We present a relationship between the
matrix measure and the real parts of the eigenvalues that make it
possible to obtain stability criteria.