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International Journal of Mathematics and Mathematical Sciences
Volume 2003 (2003), Issue 2, Pages 75-85
http://dx.doi.org/10.1155/S0161171203202295

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 Hindawi Publishing Corporation. 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.

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.