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Circuits, Systems, and Signal Processing

, Volume 39, Issue 1, pp 65–82 | Cite as

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

  • Rui Dong
  • Yonggang ChenEmail author
  • Wei Qian
Article
  • 100 Downloads

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.

Keywords

Robust \(H_\infty \) filtering Discrete-time systems Polytopic uncertainties Multiple time delays 

Notes

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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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.School of Mathematical SciencesHenan Institute of Science and TechnologyXinxiangChina
  2. 2.College of Electrical Engineering and AutomationHenan Polytechnic UniversityJiaozuoChina

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