Table of Contents
ISRN Mathematical Analysis
Volume 2011 (2011), Article ID 183795, 14 pages
http://dx.doi.org/10.5402/2011/183795
Research Article

Solutions of Higher-Order Homogeneous Linear Matrix Differential Equations for Consistent and Non-Consistent Initial Conditions: Regular Case

Department of Mathematics, National and Kapodistrian University of Athens, Athens, Greece

Received 7 March 2011; Accepted 20 April 2011

Academic Editor: T. Yamazaki

Copyright © 2011 Ioannis K. Dassios. 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

We study a class of linear matrix differential equations (regular case) of higher order whose coefficients are square constant matrices. By using matrix pencil theory and the Weierstrass canonical form of the pencil we obtain formulas for the solutions and we show that the solution is unique for consistent initial conditions and infinite for nonconsistent initial conditions. Moreover we provide some numerical examples. These kinds of systems are inherent in many physical and engineering phenomena.