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Improved Results on Delay-Dependent \(H_\infty \) Control for Uncertain Systems with Time-Varying Delays

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Abstract

This paper deals with the problem of delay-dependent robust \(H_\infty \) control for uncertain systems with time-varying delays and norm-bounded parameter uncertainties. Firstly, some new delay-dependent stability criteria are proposed by exploiting a new Lyapunov–Krasovskii functional and free-weighting matrices method. Secondly, based on the criteria obtained, a delay-dependent criterion for the existence of a memoryless state feedback \(H_\infty \) controller that ensures asymptotic stability and a prescribed \(H_\infty \) performance level of the closed-loop system for all admissible uncertainties is proposed in terms of linear matrix inequalities (LMIs). These developed results enjoy much less conservatism than the existing ones due to the introduction of delay segmentation approach to estimate the upper bound of the derivative of Lyapunov functional without ignoring some useful terms that take into account information of the time-delay. Finally, numerical examples are provided to demonstrate the effectiveness and benefits of the proposed method.

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Acknowledgments

This work was jointly supported by the Alexander von Humboldt Foundation of Germany (Fellowship CHN/1163390), the National Natural Science Foundation of China (61374080), the Natural Science Foundation of Jiangsu Province (BK20161552), Qing Lan Project of Jiangsu Province and the Priority Academic Program Development of Jiangsu Higher Education Institutions.

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Authors and Affiliations

  1. Ramanujan Centre for Higher Mathematics, Alagappa University, Karaikudi, 630 004, India

    R. Raja

  2. School of Mathematical Sciences and Institute of Finance and Statistics, Nanjing Normal University, Nanjing, 210023, Jiangsu, China

    Quanxin Zhu

  3. Department of Mathematics, University of Bielefeld, 33615, Bielefeld, Germany

    Quanxin Zhu

  4. Department of Mathematics, Thiruvalluvar University, Vellore, 632 115, India

    R. Samidurai & S. Senthilraj

  5. School of Mathematics and Physics, Jiangsu University of Technology, Changzhou, 213001, Jiangsu, China

    Wei Hu

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  1. R. Raja
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  2. Quanxin Zhu
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Correspondence to Quanxin Zhu.

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Raja, R., Zhu, Q., Samidurai, R. et al. Improved Results on Delay-Dependent \(H_\infty \) Control for Uncertain Systems with Time-Varying Delays. Circuits Syst Signal Process 36, 1836–1859 (2017). https://doi.org/10.1007/s00034-016-0382-8

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  • DOI: https://doi.org/10.1007/s00034-016-0382-8

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