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Finite-Time Passification of Fractional-Order Recurrent Neural Networks with Proportional Delay and Impulses: an LMI Approach

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Mathematical Modelling and Computational Intelligence Techniques (ICMMCIT 2021)

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 376))

Abstract

This manuscript deals with the problem of passification of fractional-order neural networks (FONNs) with proportional delays and impulses in finite time. The primary contribution of this work lies in the fact that the concept of finite-time passivity (FTP) is extended for FONNs with and without impulses for the first time. At the fore set, the notion of FTP in terms of Lyapunov function is extended to fractional-order systems. Based on the proposed definition of FTP, sufficient conditions in terms of LMI are derived to ensure the FTP of the considered FONNs. Further to this, a new lemma using comparison principle is derived using which the definition of FTP for FONNs with impulses is put forth. From these results, some new set of LMI conditions for the considered system to be finite-time stable (FTS) is derived. Finally, theoretical results are verified via a numerical example.

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Acknowledgements

Funding: This work was supported by UGC-SAP (DSA-I), New Delhi, India, File No.: F.510/7/DSA-1/2015(SAP-I).

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Authors and Affiliations

  1. Department of Mathematics, The Gandhigram Rural Institute (Deemed to be University), Gandhigram, Tamil Nadu, 624302, India

    N. Padmaja & P. Balasubramaniam

Authors
  1. N. Padmaja
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  2. P. Balasubramaniam
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Editor information

Editors and Affiliations

  1. Department of Mathematics, The Gandhigram Rural Institute (Deemed to be University), Dindigul, Tamil Nadu, India

    P. Balasubramaniam

  2. Institute of Computer Science and Digital Innovation, UCSI University, Kuala Lumpur, Malaysia

    Kuru Ratnavelu

  3. Department of Mathematics, Faculty of Science, Maejo University, Chiang Mai, Thailand

    Grienggrai Rajchakit

  4. Department of Mathematics, The Gandhigram Rural Institute (Deemed to be University), Dindigul, Tamil Nadu, India

    G. Nagamani

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Padmaja, N., Balasubramaniam, P. (2021). Finite-Time Passification of Fractional-Order Recurrent Neural Networks with Proportional Delay and Impulses: an LMI Approach. In: Balasubramaniam, P., Ratnavelu, K., Rajchakit, G., Nagamani, G. (eds) Mathematical Modelling and Computational Intelligence Techniques. ICMMCIT 2021. Springer Proceedings in Mathematics & Statistics, vol 376. Springer, Singapore. https://doi.org/10.1007/978-981-16-6018-4_13

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