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Global Exponential Stability of Inertial Cohen–Grossberg Neural Networks with Time-Varying Delays via Feedback and Adaptive Control Schemes: Non-reduction Order Approach

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Abstract

In this article, the problem is dealt for the global exponential stability of delayed Cohen–Grossberg inertial neural networks (CGINNs) by constructing a new innovative Lyapunov functional instead of the traditional reduced-order method. The newly constructed Lyapunov functional together with two different control schemes and the inequality technique, analyze the global exponential stability for the considered second-order inertial neural networks (INNs). The dynamical behavior of CGINNs in the present study is new and different from the reduced-order method through variable substitution. The simpler inequalities in the proposed method help to achieve the stability criteria of CGINNs in a easier way as compared to the existing results. Finally, a numerical example is presented to validate the efficiency of the proposed method.

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Acknowledgements

The authors are extending their heartfelt thanks to the revered reviewers for their constructive suggestions towards the improvement of the article. The author Subir Das acknowledges the project grant provided by the SERB, Government of India under the MATRICS scheme (File no: MTR/2020/000053).

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Authors and Affiliations

  1. Department of Mathematical Sciences, Indian Institute of Technology (BHU), Varanasi, 221005, India

    Sunny Singh, Umesh Kumar & Subir Das

  2. School of Mathematics, Southeast University, Nanjing, 210096, China

    Jinde Cao

  3. Yonsei Frontier Lab, Yonsei University, Seoul, 03722, South Korea

    Jinde Cao

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  1. Sunny Singh
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Correspondence to Jinde Cao.

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Singh, S., Kumar, U., Das, S. et al. Global Exponential Stability of Inertial Cohen–Grossberg Neural Networks with Time-Varying Delays via Feedback and Adaptive Control Schemes: Non-reduction Order Approach. Neural Process Lett 55, 4347–4363 (2023). https://doi.org/10.1007/s11063-022-11044-9

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