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An Improved Approach to Robust \(H_\infty \) Filtering for Uncertain Discrete-Time Systems with Multiple Delays

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Abstract

This paper is concerned with the robust \(H_\infty \) filtering problem for a class of discrete-time systems with polytopic uncertainties and multiple time delays. Different from the most existing techniques, the novel augmented Lyapunov–Krasovskii functionals are constructed by incorporating the relationships between multiple time delays. Based on the proposed functionals and the Wirtinger-based inequality, sufficient conditions are first established under which the filtering error system is asymptotically stable and has an prescribed \(H_\infty \) performance level. Then, the adjusting parameters are introduced such that the filter gains can be effectively obtained by solving certain linear matrix inequalities. Finally, two numerical examples are given to demonstrate the effectiveness and the benefit of the proposed approach.

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Acknowledgements

This work was supported in part by the National Natural Science Foundation of China under Grant 61773156, in part by the Program for Science and Technology Innovation Talents in the Universities of Henan Province of China (No. 19HASTIT028) and in part by the China Postdoctoral Science Foundation (No. 2017M612394).

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Authors and Affiliations

  1. School of Mathematical Sciences, Henan Institute of Science and Technology, Xinxiang, 453003, China

    Rui Dong & Yonggang Chen

  2. College of Electrical Engineering and Automation, Henan Polytechnic University, Jiaozuo, 454000, China

    Wei Qian

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  1. Rui Dong
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  2. Yonggang Chen
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  3. Wei Qian
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Correspondence to Yonggang Chen.

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Dong, R., Chen, Y. & Qian, W. An Improved Approach to Robust \(H_\infty \) Filtering for Uncertain Discrete-Time Systems with Multiple Delays. Circuits Syst Signal Process 39, 65–82 (2020). https://doi.org/10.1007/s00034-019-01162-6

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