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Mathematical Problems in Engineering
Volume 2013, Article ID 163769, 8 pages
Research Article

Robust Control for Discrete-Time Stochastic Interval System with Time Delay

1Hubei Province Key Laboratory of Systems Science in Metallurgical Process, Wuhan University of Science & Technology, Wuhan 430081, China
2School of Hydropower & Information Engineering, Huazhong University of Science & Technology, Wuhan 430074, China
3School of Automation, Huazhong University of Science & Technology, Wuhan 430074, China

Received 23 April 2013; Accepted 26 August 2013

Academic Editor: Bo Shen

Copyright © 2013 Shengchun Yu 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 robust control problem for discrete-time stochastic interval system (DTSIS) with time delay is investigated in this paper. The stochastic interval system is equivalently transformed into a kind of stochastic uncertain time-delay system firstly. By constructing the appropriate Lyapunov-Krasovskii functional, the sufficient conditions for the existence of the robust controller for DTSIS are obtained in terms of linear matrix inequality (LMI) form, and the robust controller is designed. Finally, a numerical example with simulation is given to show the effectiveness and correctness of the designed robust controller.