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Adaptive \(H_{\infty }\) Integral Sliding Mode Control for Uncertain Singular Time-Delay Systems Based on Observer

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Abstract

This paper is concerned with the robust \(H_{\infty }\) control for a class of uncertain singular time-delay systems via a novel sliding mode observer scheme. Firstly, a particularly non-fragile observer is introduced to estimate the unmeasured states, and a novel integral sliding surface function is presented. Then, a sufficient condition for the admissibility and specified \(H_{\infty }\) performance of the resultant sliding mode dynamics of the closed-loop systems is derived in terms of linear matrix inequality. At last, the finite-time reachability of the predesigned sliding surface is guaranteed by utilizing the adaptive sliding mode control law from the initial time. An illustrative example is provided to verify the potential and superiority of the method with comparisons.

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Acknowledgements

The authors would like to thank the editors and the anonymous reviewers for their constructive comments which helped to improve the quality and presentation of this paper. This work was partially supported by the National Natural Science Foundation of China under Grants 61374079, 61473097, 61603204, 41306002, the Natural Science Foundation of Shandong Province under grant ZR2016FP03 and the Qingdao Application Basic Research Project under Grant 16-5-1-22-jch.

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Authors and Affiliations

  1. School of Mathematical Sciences, Ocean University of China, Qingdao, 266100, People’s Republic of China

    Zhen Liu & Cunchen Gao

  2. Institute for Sustainable Manufacturing, College of Engineering, University of Kentucky, Lexington, KY, 40506, USA

    Zhen Liu

  3. School of Automation and Electrical Engineering, Qingdao University, Qingdao, 266071, People’s Republic of China

    Lin Zhao

  4. School of Computer and Information Engineering, Henan University of Economics and Law, Zhengzhou, 450046, People’s Republic of China

    Huimin Xiao

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  1. Zhen Liu
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  3. Huimin Xiao
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  4. Cunchen Gao
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Correspondence to Zhen Liu.

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Liu, Z., Zhao, L., Xiao, H. et al. Adaptive \(H_{\infty }\) Integral Sliding Mode Control for Uncertain Singular Time-Delay Systems Based on Observer. Circuits Syst Signal Process 36, 4365–4387 (2017). https://doi.org/10.1007/s00034-017-0536-3

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