Journal of Applied Mathematics
Volume 2012 (2012), Article ID 749847, 11 pages
http://dx.doi.org/10.1155/2012/749847
Research Article

A Matrix Method for Determining Eigenvalues and Stability of Singular Neutral Delay-Differential Systems

Jian Ma,1,2 Baodong Zheng,1 and Chunrui Zhang2

1Department of Mathematics, Harbin Institute of Technology, Harbin 150001, China
2Department of Mathematics, Northeast Forestry University, Harbin 150040, China

Received 29 November 2011; Revised 6 April 2012; Accepted 8 April 2012

Academic Editor: Zhiwei Gao

Copyright © 2012 Jian Ma 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.

Abstract

The eigenvalues and the stability of a singular neutral differential system with single delay are considered. Firstly, by applying the matrix pencil and the linear operator methods, new algebraic criteria for the imaginary axis eigenvalue are derived. Second, practical checkable criteria for the asymptotic stability are introduced.