Abstract and Applied Analysis
Volume 2012 (2012), Article ID 490903, 11 pages
Research Article

Controllability Analysis of Linear Discrete Time Systems with Time Delay in State

1Department of Mathematics and Physics, Beijing Institute of Petrochemical Technology, Beijing 102617, China
2State Key Laboratory for Turbulence and Complex Systems, College of Engineering, Peking University, Beijing 100871, China
3School of Electrical and Electronics Engineering, East China Jiaotong University, Nanchang 330013, China
4School of Electric and Information Engineering, Guangxi University of Science and Technology, Liuzhou 545006, China
5Guangxi Key Laboratory of Automobile Components and Vehicle Technology, Liuzhou 545006, China

Received 27 August 2012; Accepted 10 October 2012

Academic Editor: Valery Y. Glizer

Copyright © 2012 Hong Shi 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.


The controllability issues for linear discrete-time systems with delay in state are addressed. By introducing a new concept, the minimum controllability realization index (MinCRI), the characteristic of controllability is revealed. It is proved that the MinCRI of a system with state delay exists and is finite. Based on this result, a necessary and sufficient condition for the controllability of discrete-time linear systems with state delay is established.