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Mixed H∞/passivity based stability analysis of fractional-order gene regulatory networks with variable delays

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  • Padmaja, N.
  • Balasubramaniam, P.

Abstract

In this paper, we derive delay and fractional-order dependent sufficient conditions for fractional-order gene regulatory networks (FOGRNs) with time-varying delays to be stable with H∞/passivity performance. Distinct from the existing works on delayed FOGRNs, the Lyapunov-Krasovskii functional (LKF) is suitably structured so that the delay functions can be non-differentiable or even have jump type discontinuities. Further, the positive-definiteness condition is relaxed for the matrices involved in LKF. A new set of linear matrix inequality (LMI) conditions that ensure the stability of FOGRNs with certain H∞/passivity performance level is derived using various results on fractional derivatives/integrals and convex property of LMIs. Finally, the results obtained are verified with existing FOGRNs via numerical simulations.

Suggested Citation

  • Padmaja, N. & Balasubramaniam, P., 2022. "Mixed H∞/passivity based stability analysis of fractional-order gene regulatory networks with variable delays," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 192(C), pages 167-181.
    • Handle: RePEc:eee:matcom:v:192:y:2022:i:c:p:167-181
    DOI: 10.1016/j.matcom.2021.08.023
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    1. Cao, Yang & Samidurai, R. & Sriraman, R., 2019. "Robust passivity analysis for uncertain neural networks with leakage delay and additive time-varying delays by using general activation function," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 155(C), pages 57-77.
    2. Syed Ali, M. & Narayanan, G. & Saroha, Sumit & Priya, Bandana & Thakur, Ganesh Kumar, 2021. "Finite-time stability analysis of fractional-order memristive fuzzy cellular neural networks with time delay and leakage term," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 185(C), pages 468-485.
    3. Liping Chen & Tingting Li & YangQuan Chen & Ranchao Wu & Suoliang Ge, 2019. "Robust passivity and feedback passification of a class of uncertain fractional-order linear systems," International Journal of Systems Science, Taylor & Francis Journals, vol. 50(6), pages 1149-1162, April.
    4. Michael B. Elowitz & Stanislas Leibler, 2000. "A synthetic oscillatory network of transcriptional regulators," Nature, Nature, vol. 403(6767), pages 335-338, January.
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    Cited by:

    1. Qiu, Hongling & Cao, Jinde & Liu, Heng, 2023. "Passivity of fractional-order coupled neural networks with interval uncertainties," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 205(C), pages 845-860.
    2. Aghayan, Zahra Sadat & Alfi, Alireza & Mousavi, Yashar & Kucukdemiral, Ibrahim Beklan & Fekih, Afef, 2022. "Guaranteed cost robust output feedback control design for fractional-order uncertain neutral delay systems," Chaos, Solitons & Fractals, Elsevier, vol. 163(C).

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