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Journal of Control Science and Engineering
Volume 2016, Article ID 5214147, 7 pages
Research Article

Reachable Set Estimation for Discrete-Time Systems with Interval Time-Varying Delays and Bounded Disturbances

1School of Mathematics and Computer Science, Wuhan Polytechnic University, Wuhan 430023, China
2School of Automation, Huazhong University of Science and Technology, Wuhan 430074, China

Received 1 October 2016; Accepted 23 October 2016

Academic Editor: Xian Zhang

Copyright © 2016 Jiemei Zhao and Yin Sheng. 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 reachable set estimation problem for discrete-time systems with delay-range-dependent and bounded disturbances is investigated. A triple-summation term, the upper bound, and the lower bound of time-varying delay are introduced into the Lyapunov function. In this case, an improved delay-range-dependent criterion is established for the addressed problem by constructing the appropriate Lyapunov functional, which guarantees that the reachable set of discrete-time systems with time-varying delay and bounded peak inputs is contained in the ellipsoid. It is worth mentioning that the initial value of the system does not need to be zero. Then, the reachable set estimation problem for time-delay systems with polytopic uncertainties is investigated. The effectiveness and the reduced conservatism of the derived results are demonstrated by an illustrative example.