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Robust exponential stabilization of delayed neural networks with external disturbance via extended reciprocally convex matrix inequality

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Abstract

The paper investigates the robust exponential stabilization of delayed neural networks (NNs) with parameter uncertainties and external disturbance. Firstly, the delay dependent state feedback controller is designed and an appropriate Lyapunov–Krasovskii functional (LKF) is constructed for the considered closed-loop system. The delay dependent stability criteria are obtained using auxiliary function-based integral inequality and extended reciprocally convex matrix inequality. This stability criteria ensure that the closed-loop system is robust exponential stable with a guaranteed \(H_{\infty }\) performance level \(\gamma \) for all admissible uncertainties. The delay dependent controller gain matrices can be obtained by solving the linear matrix inequalities (LMIs). The stability criteria are given for non differentiable delay and the system without uncertainties respectively. Finally, three simulation examples are addressed to demonstrate the effectiveness of the proposed methods.

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Acknowledgements

The authors would like to thank the associate editors and the reviewers for their insightful and constructive comments, which helped to enrich the content and improve the presentation of the results in this paper. This research was supported by the National Natural Science Foundation of China under Grant No. 11971303 and the Natural Science Foundation of Shanghai under Grant No. 21ZR1426400.

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Authors and Affiliations

  1. Department of Mathematics, Shanghai University, Shanghai, 200444, China

    Liangliang Guo

  2. School of Mathematical Sciences, Tiangong University, Tianjin, 300387, China

    Yali Dong

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  1. Liangliang Guo
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  2. Yali Dong
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Correspondence to Liangliang Guo.

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Communicated by Marcos Eduardo Valle.

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Guo, L., Dong, Y. Robust exponential stabilization of delayed neural networks with external disturbance via extended reciprocally convex matrix inequality. Comp. Appl. Math. 41, 185 (2022). https://doi.org/10.1007/s40314-022-01854-x

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  • DOI: https://doi.org/10.1007/s40314-022-01854-x

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