Abstract and Applied Analysis
Volume 2010 (2010), Article ID 948764, 27 pages
doi:10.1155/2010/948764
Research Article

Spectral Properties and Finite Pole Assignment of Linear Neutral Systems in Banach Spaces

Xuewen Xia1 and Kai Liu2

1Faculty of Science, Hunan Institute of Engineering, Xiangtan, Hunan 411104, China
2Division of Statistics and Probability, Department of Mathematical Sciences, The University of Liverpool, Peach Street, Liverpool L69 7ZL, UK

Received 28 March 2010; Accepted 13 May 2010

Academic Editor: Viorel Barbu

Copyright © 2010 Xuewen Xia and Kai Liu. 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 will consider a pole assignment problem for a class of linear neutral functional differential equations in Banach spaces. We will think of the neutral system studied as that of involving no time delays and reduce the study of adjoint semigroups and spectral properties of neutral equations to those of Cauchy problems. Under the assumption that both the control and eigenspace of pole are finite dimensional, we establish the rank conditions for finite pole assignability.