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Journal of Applied Mathematics
Volume 2013, Article ID 146010, 9 pages
Research Article

Controllability Criteria for Linear Fractional Differential Systems with State Delay and Impulses

1Department of Mathematics, Southeast University, Nanjing, Jiangsu 210096, China
2Department of Mathematics, Anqing Normal University, Anqing, Anhui 246133, China
3Department of Mathematics, King Abdulaziz University, Jeddah 21589, Saudi Arabia
4School of Mathematical Sciences, Anhui University, Hefei, Anhui 230039, China

Received 8 April 2013; Accepted 14 May 2013

Academic Editor: Francisco J. Marcellán

Copyright © 2013 Hai Zhang 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.


This paper is concerned with the controllability of linear fractional differential systems with delay in state and impulses. The factors of such systems including fractional derivative, impulses, and delay are taken into account synchronously. The expression of state response for such systems is derived, and the sufficient and necessary conditions of controllability criteria are established. Both the proposed criteria and illustrative examples show that the controllability property of the linear systems is dependent neither on the order of fractional derivative, on delay nor on impulses.