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Mathematical Problems in Engineering
Volume 2016, Article ID 7843940, 11 pages
Research Article

Robust Quadratic Stabilizability and Control of Uncertain Linear Discrete-Time Stochastic Systems with State Delay

1College of Information and Control Engineering, China University of Petroleum (East China), Qingdao 266510, Shandong Province, China
2College of Electrical Engineering and Automation, Shandong University of Science and Technology, Qingdao 266590, Shandong Province, China

Received 20 May 2016; Revised 9 August 2016; Accepted 5 October 2016

Academic Editor: Abdellah Benzaouia

Copyright © 2016 Xiushan Jiang 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 mainly discusses the robust quadratic stability and stabilization of linear discrete-time stochastic systems with state delay and uncertain parameters. By means of the linear matrix inequality (LMI) method, a sufficient condition is, respectively, obtained for the stability and stabilizability of the considered system. Moreover, we design the robust state feedback controllers such that the system with admissible uncertainties is not only quadratically internally stable but also robust controllable. A sufficient condition for the existence of the desired robust controller is obtained. Finally, an example with simulations is given to verify the effectiveness of our theoretical results.