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Mathematical Problems in Engineering
Volume 2019, Article ID 5368013, 14 pages
https://doi.org/10.1155/2019/5368013
Research Article

Robust Admissibilization for Discrete-Time Singular Systems with Time-Varying Delay

1School of Information and Automation Engineering, Qingdao University of Technology, Qingdao 266555, China
2School of Information Engineering, Weifang Vocational College, Weifang 262737, China

Correspondence should be addressed to Jian Chen; moc.361@cenaj

Received 21 May 2019; Revised 22 August 2019; Accepted 30 August 2019; Published 7 November 2019

Academic Editor: Jorge Rivera

Copyright © 2019 Dongdong Wang 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.

Abstract

The problems of the admissibility and state feedback stabilization for discrete-time singular systems with interval time-varying delay and norm-bounded uncertainty are studied. The system is equivalently transformed into a new comparison form by decomposition. By taking advantage of the Seuret summation inequality, the reciprocally convex inequality, and some relaxation techniques, a delay-dependent criterion that ensures the admissibility of the concerned systems is established. The result on robust stabilization is also obtained by fixing some parameters. It should be pointed out that the results are less dependent on the parameters so that some conservatism is reduced. A numerical example is included to illustrate the effectiveness and improvement of the proposed methods.