International Journal of Mathematics and Mathematical Sciences
Volume 2003 (2003), Issue 2, Pages 75-85
doi:10.1155/S0161171203202295
Matrix measure and application to stability of matrices and interval dynamical systems
Ziad Zahreddine
Department of Basic Sciences, College of Arts and Sciences, University of Sharjah, P.O. 27272, Sharjah, United Arab Emirates
Abstract
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.