Conclusion
This study has investigated the stability of discrete-time systems with a time-varying delay. To handle the negativity condition of the forward difference of Lyapunov function, a matrix-injection-based method has been developed to convert the original negativity condition to an equivalent tractable matrix inequality by injecting a few matrices. By using this method and an augmented Lyapunov function, a stability criterion with less conservatism for the delayed linear discrete-time system has been developed. The case study via a numerical example has shown the merit of the criterion. It is predictable that the proposed method, together with the methods recently reported by [9], can further improve the results.
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Acknowledgements
This work was supported in part by National Natural Science Foundation of China (Grant Nos. 62022074, 61973284), Hubei Provincial Natural Science Foundation (Grant No. 2019CFA040), the 111 Project (Grant No. B17040), and Fundamental Research Funds for National Universities, China University of Geosciences, Wuhan.
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Appendixes A–C. The supporting information is available online at info.scichina.com and link.springer.com. The supporting materials are published as submitted, without typesetting or editing. The responsibility for scientific accuracy and content remains entirely with the authors.
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Zhang, CK., Xie, KY., He, Y. et al. Matrix-injection-based transformation method for discrete-time systems with time-varying delay. Sci. China Inf. Sci. 66, 159201 (2023). https://doi.org/10.1007/s11432-020-3221-6
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DOI: https://doi.org/10.1007/s11432-020-3221-6