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Results on finite time passivity of fractional-order quaternion-valued neural networks with time delay via linear matrix inequalities

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Abstract

This paper introduces the finite-time passivity (FTP) issue of the fractional-order delayed quaternion-valued neural networks (FOQVNNs). The notions of FTP, finite-time input strict passivity (FTISP), and finite-time output strict passivity (FTOSP) of FOQVNNs are presented on the groud of the existing definitions of FTP of fractional-order neural networks. Then, sufficient criteria to guarantee the FTP (FTISP, FTOSP) of the system are developed utilizing the given definitions, Lyapunov function theory, inequality technique, and an appropriate controller is established. Additionally, the presented finite-time stability criterion and setting-time are according to the concept of FTP. At last, the significance of the theoretical results are tested by a simulation experiment.

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References

  1. Chen, Y., Zhang, N., Yang, J.: A survey of recent advances on stability analysis, state estimation and synchronization control for neural networks. Neurocomputing 515, 26–36 (2023)

    Article  Google Scholar 

  2. Wang, L., Bian, Y., Guo, Z., Hu, M.: Lag H\(\infty \) synchronization in coupled reaction-diffusion neural networks with multiple state or derivative couplings. Neural Netw. 156, 179–192 (2022)

    Article  Google Scholar 

  3. Ping, J., Zhu, S., Liu, X.: Finite/fixed-time synchronization of memristive neural networks via event-triggered control. Knowl.-Based Syst. 1258, 110013 (2022)

    Article  Google Scholar 

  4. Zou, C., Zhang, L., Hu, X., Wang, Z., Wik, T., Pecht, M.: A review of fractional-order techniques applied to lithium-ion batteries, lead-acid batteries, and supercapacitors. J. Power Sources 390, 286–296 (2018)

    Article  Google Scholar 

  5. Boukhouima, A., Hattaf, K., Lotfi, E.M., Mahrouf, M., Torres, D.F.M., Yousfi, N.: Lyapunov functions for fractional-order systems in biology: methods and applications. Chaos Solitons Fractals 140, 110224 (2020)

    Article  MathSciNet  Google Scholar 

  6. Yilmaz, B.: A new type electromagnetic curves in optical fiber and rotation of the polarization plane using fractional calculus. Optik 247, 168026 (2021)

    Article  Google Scholar 

  7. Coulibaly, S., Kamsu-Foguem, B., Kamissoko, D., Traore, D.: Deep convolution neural network sharing for the multi-label images classification. Mach. Learn. Appl. 10, 100422 (2022)

    Google Scholar 

  8. Sanderson, M., Bulloch, A.G.M., Wang, J., Williamson, T., Patten, S.B.: Predicting death by suicide using administrative health care system data: can feedforward neural network models improve upon logistic regression models? J. Affect. Disord. 257, 741–747 (2019)

    Article  Google Scholar 

  9. Capanema, C.G.S., de Oliveira, G.S., Silva, F.A., Silva, T.R.M.B., Loureiro, A.A.F.: Combining recurrent and graph neural networks to predict the next place’s category. Ad Hoc Netw. 138, 103016 (2023)

    Article  Google Scholar 

  10. Xiao, J., Wu, L., Wu, A., Zeng, Z., Zhang, Z.: Novel controller design for finite-time synchronization of fractional-order memristive neural networks. Neurocomputing 512, 494–502 (2022)

    Article  Google Scholar 

  11. Xiao, J., Guo, X., Li, Y., Wen, S., Shi, K., Tang, Y.: Extended analysis on the global Mittag–Leffler synchronization problem for fractional-order octonion-valued BAM neural networks. Neural Netw. 154, 491–507 (2022)

    Article  Google Scholar 

  12. Tan, H., Wu, J., Bao, H.: Event-triggered impulsive synchronization of fractional-order coupled neural networks. Appl. Math. Comput. 429, 127244 (2022)

    MathSciNet  Google Scholar 

  13. Hui, M., Wei, C., Zhang, J., Iu, H.H.C., Yao, R., Bai, L.: Finite-time synchronization of fractional-order memristive neural networks via feedback and periodically intermittent control. Commun. Nonlinear Sci. Numer. Simul. 116, 106822 (2023)

    Article  MathSciNet  Google Scholar 

  14. Ren, S., Wu, J., Wei, P.: Passivity and pinning passivity of coupled delayed reaction-diffusion neural networks with Dirichlet boundary conditions. Neural Process Lett. 45, 869–885 (2017)

    Article  Google Scholar 

  15. Chen, W., Huang, Y., Ren, S.: Passivity and robust passivity of delayed Cohen–Grossberg neural networks with and without reaction–diffusion terms. Circuits Syst. Signal Process. 37, 2772–2804 (2018)

    Article  MathSciNet  Google Scholar 

  16. Huang, Y., Ren, S.: Passivity and passivity-based synchronization of switched coupled reaction–diffusion neural networks with state and spatial diffusion couplings. Neural Process. Lett. 47, 347–363 (2018)

    Google Scholar 

  17. Wang, J., Zhang, X., Wen, G., Chen, Y., Wu, H.: Passivity and finite-time passivity for multi-weighted fractional-order complex networks with fixed and adaptive couplings. IEEE Trans. Neural Netw. Learn. Syst. 34, 894–908 (2023)

    Article  MathSciNet  Google Scholar 

  18. Liu, C.G., Wang, J.L., Wu, H.N.: Finite-time passivity for coupled fractional-order neural networks with multistate or multiderivative couplings. IEEE Trans. Neural Netw. Learn. Syst. 20, 1–12 (2021)

    Google Scholar 

  19. Xiao, J., Zeng, Z.: Finite-time passivity of neural networks with time varying delay. J. Frankl. Inst. 357, 2437–2456 (2020)

    Article  MathSciNet  Google Scholar 

  20. Babu, N.R., Balasubramaniam, P.: Master-slave synchronization of a new fractal-fractional order quaternion-valued neural networks with time-varying delays. Chaos Solitons Fractals 162, 112478 (2022)

    Article  MathSciNet  Google Scholar 

  21. Padmaja, N., Balasubramaniam, P.: Results on passivity analysis of delayed fractional-order neural networks subject to periodic impulses via refined integral inequalities. Comput. Appl. Math. 41(4), 136 (2022)

    Article  MathSciNet  Google Scholar 

  22. Balasubramaniam, P., Nagamani, G.: A delay decomposition approach to delay-dependent passivity analysis for interval neural networks with time-varying delay. Neurocomputing 74, 1646–1653 (2011)

    Article  Google Scholar 

  23. Zhang, X., Li, H., Kao, Y., Zhang, L., Jiang, H.: Global Mittag–Leffler synchronization of discrete-time fractional-order neural networks with time delays. Appl. Math. Comput. 433, 127417 (2022)

    MathSciNet  Google Scholar 

  24. Aravind, R.V., Balasubramaniam, P.: Stability criteria for memristor-based delayed fractional-order Cohen–Grossberg neural networks with uncertainties. J. Comput. Appl. Math. 420, 114764 (2023)

    Article  MathSciNet  Google Scholar 

  25. Peng, Q., Jian, J.: Synchronization analysis of fractional-order inertial-type neural networks with time delays. Math. Comput. Simul. 205, 62–77 (2023)

    Article  MathSciNet  Google Scholar 

  26. Stamova, I., Stamov, T., Stamov, G.: Lipschitz stability analysis of fractional-order impulsive delayed reaction–diffusion neural network models. Chaos Solitons Fractals 162, 112474 (2022)

    Article  MathSciNet  Google Scholar 

  27. Liu, C., Wang, J.: Passivity of fractional-order coupled neural networks with multiple state/derivative couplings. Neurocomputing 455, 379–389 (2021)

    Article  Google Scholar 

  28. Padmaja, N., Balasubramaniam, P.: New delay and order-dependent passivity criteria for impulsive fractional-order neural networks with switching parameters and proportional delays. Neurocomputing 454, 113–123 (2021)

    Article  Google Scholar 

  29. Yan, M., Jian, J., Zheng, S.: Passivity analysis for uncertain bam inertial neural networks with time-varying delays. Neurocomputing 435, 114–125 (2021)

    Article  Google Scholar 

  30. Xiao, S., Wang, Z., Wang, C.: Passivity analysis of fractional-order neural networks with interval parameter uncertainties via an interval matrix polytope approach. Neurocomputing 477, 96–103 (2022)

    Article  Google Scholar 

  31. Thuan, M.V., Huong, D.C., Hong, D.T.: New results on robust finite-time passivity for fractional-order neural networks with uncertainties. Neural Process. Lett. 50, 1065–1078 (2019)

    Article  Google Scholar 

  32. Shafiya, M., Nagamani, G.: New finite-time passivity criteria for delayed fractional-order neural networks based on Lyapunov function approach. Chaos Solitons Fractals 158, 112005 (2022)

    Article  MathSciNet  Google Scholar 

  33. Podlubny, I.: Fractional Differential Equations. Academic Press, New York (1999)

    Google Scholar 

  34. Li, H., Zhang, L., Hu, C., Jiang, H., Cao, J.: Global Mittag–Leffler synchronization of fractional-order delayed quaternion-valued neural networks: direct quaternion approach. Appl. Math. Comput. 373, 125020 (2020)

    MathSciNet  Google Scholar 

  35. Song, Q., Chen, Y., Zhao, Z., Liu, Y., Alsaadi, F.E.: Robust stability of fractional-order quaternion-valued neural networks with neutral delays and parameter uncertainties. Neurocomputing 420, 70–81 (2021)

    Article  Google Scholar 

  36. Huang, X., Lin, W., Yang, B.: Global finite-time stabilization of a class of uncertain nonlinear systems. Automatica 41, 881–888 (2005)

    Article  MathSciNet  Google Scholar 

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Acknowledgements

This work was supported by the National Natural Science Foundation of China (Grant No. 61573096), the Natural Science Foundation of Anhui Province (Grant No. 1908085MA01), the Excellent Young Talents Fund Program of Higher Education Institutions of Anhui Province (Grants No. 2023AH050502).

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Author notes

  1. Zhang Weiwei, Zhang Hai, Zhang Hongmei and Cao Jinde contributed equally to this work.

Authors and Affiliations

  1. School of Mathematics and Physics, Anqing Normal University, Anqing, 246133, China

    Shang Weiying, Zhang Weiwei, Zhang Hai & Zhang Hongmei

  2. Department of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing, 210093, China

    Zhang Weiwei

  3. International Joint Research Center of Simulation and Control for Population Ecology of Yangtze River in Anhui, Anqing Normal University, Anqing, 246133, China

    Zhang Weiwei

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

    Cao Jinde

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  1. Shang Weiying
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Correspondence to Zhang Weiwei.

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Weiying, S., Weiwei, Z., Hai, Z. et al. Results on finite time passivity of fractional-order quaternion-valued neural networks with time delay via linear matrix inequalities. J. Appl. Math. Comput. 69, 4759–4777 (2023). https://doi.org/10.1007/s12190-023-01951-y

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