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Improved results on stability and \(H_{\infty }\) performance analysis for discrete-time neural networks with time-varying delay

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Abstract

In this paper, to develop less conservative delay-dependent stability criterion and the method for \(H_{\infty }\) performance analysis, the problem of stability and \(H_{\infty }\) performance for discrete-time neural networks with time-varying delay is investigated. Inequality is an important tool for stability and \(H_{\infty }\) performance analysis. To reduce the conservatism of some existing inequalities, an improved reciprocally convex inequality is proved. This inequality is related to the quadratic of delay and encompasses some existing inequalities as its special cases. Based on the proposed reciprocally convex approach, a novel free-matrix-based summation inequality is derived. A delay-product-type Lyapunov–Krasovskii functional (LKF) term is introduced. By utilizing the constructed LKF, information of time delay, and the proposed reciprocally convex approach, two improved sufficient conditions for stability and \(H_{\infty }\) performance of discrete-time neural networks with time-varying delay are derived in terms of linear matrix inequalities (LMIs), respectively. Finally, several numerical examples are provided to illustrate the effectiveness and benefits of our proposed approach.

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Data sharing is not applicable to this article as no datasets were generated or analysed during the current study.

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Acknowledgements

The authors would like to thank the editor and anonymous reviewers for their valuable comments and suggestions.

Funding

This work is partly supported by the National Natural Science Foundation of China under Grant nos. 61773404 and 61271355, Fundamental Research Funds for the Central Universities of Central South University no. 2018zzts098, and Scientific Research Fund of Hunan Provincial Education Department no. 20C0349.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Central South University, Changsha, 410083, China

    Qiao Chen, Xinge Liu & Peiyu Guo

  2. School of Science, Hunan City University, Yiyang, 413000, Hunan, China

    Qiao Chen & Xiayun Li

  3. Zhongnan Hospital of Wuhan University, Wuhan, 430071, China

    Hua Liu

Authors
  1. Qiao Chen
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  2. Xinge Liu
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  3. Peiyu Guo
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  4. Hua Liu
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  5. Xiayun Li
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All authors contributed equally and significantly in writing this paper. All authors read and approved the final manuscript.

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Correspondence to Hua Liu.

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The authors declared that they have no conflicts of interest to this work.

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Communicated by Graçaliz Pereira Dimuro.

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Chen, Q., Liu, X., Guo, P. et al. Improved results on stability and \(H_{\infty }\) performance analysis for discrete-time neural networks with time-varying delay. Comp. Appl. Math. 41, 206 (2022). https://doi.org/10.1007/s40314-022-01902-6

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