Abstract and Applied Analysis
Volume 2013 (2013), Article ID 975461, 5 pages
Research Article

Controllability of Linear Discrete-Time Systems with Both Delayed States and Delayed Inputs

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

Received 29 November 2012; Accepted 31 January 2013

Academic Editor: Valery Y. Glizer

Copyright © 2013 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 discrete-time linear systems with delay in state and control are addressed. By introducing a new concept, the controllability realization index (CRI), the characteristic of controllability is revealed. An easily testable necessary and sufficient condition for the controllability of discrete-time linear systems with state and control delay is established.