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Delay-Independent and Dependent \({\mathcal {L}}_{2}-{\mathcal {L}}_{\infty }\) Filter Design for Time-Delay Reaction–Diffusion Switched Hopfield Networks

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Abstract

In this paper, we investigate the issue of \({\mathcal {L}}_{2}-{\mathcal {L}}_{\infty }\) filtering for time-delay reaction–diffusion switched Hopfield networks. Our main focus is on the design of a Luenberger estimator so that the filtering-error system not only is exponentially stable in the absence of external disturbance, but also possesses a predefined \({\mathcal {L}}_{2}-{\mathcal {L}}_{\infty }\) disturbance rejection level under the zero initial condition. With the aid of Lyapunov–Krasovskii functionals, several integral inequalities, and in conjunction with the free-weight matrix technique, both delay-independent and dependent design strategies are developed, where the required gains can be acquired through the feasible solution of linear matrix inequalities. To demonstrate the applicability and lower conservatism of the present design strategies, an example with numerical comparison is provided.

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References

  1. C.K. Ahn, M.K. Song, \({\cal{L} }_{2}-{\cal{L} }_{\infty }\) filtering for time-delayed switched Hopfield neural networks. Int. J. Innov. Comput. Inf. Control 7(4), 1831–1844 (2011)

    Google Scholar 

  2. M.S. Ali, J. Yogambigai, O. Kwon, Finite-time robust passive control for a class of switched reaction-diffusion stochastic complex dynamical networks with coupling delays and impulsive control. Int. J. Syst. Sci. 49(4), 718–735 (2018)

    Article  MathSciNet  MATH  Google Scholar 

  3. P. Balasubramaniam, V. Vembarasan, R. Rakkiyappan, Delay-dependent robust exponential state estimation of Markovian jumping fuzzy Hopfield neural networks with mixed random time-varying delays. Commun. Nonlinear Sci. Numer. Simul. 16(4), 2109–2129 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  4. I.A. Basheer, M. Hajmeer, Artificial neural networks: fundamentals, computing, design, and application. J. Microbiol. Meth. 43(1), 3–31 (2000)

    Article  Google Scholar 

  5. J. Cao, R. Rakkiyappan, K. Maheswari, A. Chandrasekar, Exponential \({\cal{H} }_{\infty }\) filtering analysis for discrete-time switched neural networks with random delays using sojourn probabilities. Sci. China Tech. Sci. 59(3), 387–402 (2016)

    Article  Google Scholar 

  6. Q. Chen, X. Liu, F. Wang, Improved results on \({\cal{L} }_{2}-{\cal{L} }_{\infty }\) state estimation for neural networks with time-varying delay. Circuits Syst. Signal Process. 41, 122–146 (2022)

    Article  Google Scholar 

  7. S. Chen, G. Song, B. Zheng, T. Li, Finite-time synchronization of coupled reaction-diffusion neural systems via intermittent control. Automatica 109, 108564 (2019)

    Article  MathSciNet  MATH  Google Scholar 

  8. L.V. Fausett, Fundamentals of Neural Networks: Architectures, Algorithms and Applications (Prentice-Hall, Englewood Cliffs, NJ, 1994)

    MATH  Google Scholar 

  9. K. Gu, J. Chen, V.L. Kharitonov, Stability of Time-Delay Systems (Birkhauser, Boston, MA, 2003)

    Book  MATH  Google Scholar 

  10. Y. Hong, H. Bin, Z. Huang, Synchronization of state-switching Hopfield-type neural networks: a quantized level set approach. Chaos Solitons Fractals 129, 16–24 (2019)

    Article  MathSciNet  MATH  Google Scholar 

  11. J.J. Hopfield, D.W. Tank, “Neural’’ computation of decisions in optimization problems. Biol. Cybern. 52(3), 141–152 (1985)

    Article  MATH  Google Scholar 

  12. J.J. Hopfield, Neural networks and physical systems with emergent collective computational abilities. Proc. Natl. Acad. Sci. 79(8), 2554–2558 (1982)

    Article  MathSciNet  MATH  Google Scholar 

  13. L. Hou, G. Zong, Y. Wu, Robust exponential stability analysis of discrete-time switched Hopfield neural networks with time delay. Nonlinear Anal. Hybrid Syst. 5(3), 525–534 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  14. H. Huang, Y. Qu, H. Li, Robust stability analysis of switched Hopfield neural networks with time-varying delay under uncertainty. Phys. Lett. A 345(4–6), 345–354 (2005)

    Article  MATH  Google Scholar 

  15. D.C. Huong, V.T. Huynh, H. Trinh, On static and dynamic triggered mechanisms for event-triggered control of uncertain systems. Circuits Syst. Signal Process. 39, 5020–5038 (2020)

    Article  MATH  Google Scholar 

  16. H.J. Kim, J.B. Park, Y.H. Joo, Decentralized \({\cal{H} }_\infty \) sampled-data fuzzy filter for nonlinear interconnected oscillating systems with uncertain interconnections. IEEE Trans. Fuzzy Syst. 28(3), 487–498 (2020)

    Article  Google Scholar 

  17. R. Li, H. Wei, Synchronization of delayed Markovian jump memristive neural networks with reaction-diffusion terms via sampled data control. Int. J. Mach. Learn. Cybern. 7(1), 157–169 (2016)

    Article  Google Scholar 

  18. X. Liang, S. Wang, R. Wang, X. Hu, Z. Wang, Synchronization of reaction-diffusion Hopfield neural networks with s-delays through sliding mode control. Nonlinear Anal. Model. Control 27(2), 331–349 (2022)

    MathSciNet  MATH  Google Scholar 

  19. X. Liao, Y. Fu, J. Gao, X. Zhao, Stability of Hopfield neural networks with reaction-diffusion terms. Acta Electron. Sin. 28(1), 78–80 (2000)

    Google Scholar 

  20. X. Liu, Z. Li, K. Wu, Boundary Mittag–Leffler stabilization of fractional reaction-diffusion cellular neural networks. Neural Netw. 132, 269–280 (2020)

    Article  MATH  Google Scholar 

  21. Y. Liu, Z. Wang, X. Liu, Global exponential stability of generalized recurrent neural networks with discrete and distributed delays. Neural Netw. 19(5), 667–675 (2006)

    Article  MATH  Google Scholar 

  22. X. Lu, W. Chen, Z. Ruan, T. Huang, A new method for global stability analysis of delayed reaction-diffusion neural networks. Neurocomputing 317, 127–136 (2018)

    Article  Google Scholar 

  23. B. Miao, X. Li, J. Lou, J. Lu, Pinning bipartite synchronization for coupled reaction-diffusion neural networks with antagonistic interactions and switching topologies. Neural Netw. 141, 174–183 (2021)

    Article  Google Scholar 

  24. N. Ozcan, M.S. Ali, J. Yogambigai, Q. Zhu, S. Arik, Robust synchronization of uncertain Markovian jump complex dynamical networks with time-varying delays and reaction-diffusion terms via sampled-data control. J. Frank. Inst. 355(3), 1192–1216 (2018)

    Article  MathSciNet  MATH  Google Scholar 

  25. R. Rakkiyappan, S. Dharani, Sampled-data synchronization of randomly coupled reaction-diffusion neural networks with Markovian jumping and mixed delays using multiple integral approach. Neural Comput. Appl. 28(3), 449–462 (2017)

    Article  Google Scholar 

  26. R. Sakthivel, S. Santra, B. Kaviarasan, Resilient sampled-data control design for singular networked systems with random missing data. J. Frank. Inst. 355(3), 1040–1072 (2018)

    Article  MathSciNet  MATH  Google Scholar 

  27. S. Santra, M. Joby, M. Sathishkumar, S.M. Anthoni, LMI approach-based sampled-data control for uncertain systems with actuator saturation: application to multi-machine power system. Nonlinear Dyn. 107(1), 967–982 (2022)

    Article  Google Scholar 

  28. L. Shanmugam, P. Mani, R. Rajan, Y.H. Joo, Adaptive synchronization of reaction-diffusion neural networks and its application to secure communication. IEEE Trans. Cybern. 50(3), 911–922 (2020)

    Article  Google Scholar 

  29. Q. Song, Q. Yu, Z. Zhao, Y. Liu, F.E. Alsaadi, Boundedness and global robust stability analysis of delayed complex-valued neural networks with interval parameter uncertainties. Neural Netw. 103, 55–62 (2018)

    Article  MATH  Google Scholar 

  30. X. Song, J. Man, J.H. Park, S. Song, Finite-time synchronization of reaction-diffusion inertial memristive neural networks via gain-scheduled pinning control. IEEE Trans. Neural Netw. Learn. Syst. (2021). https://doi.org/10.1109/TNNLS.2021.3068734

    Article  Google Scholar 

  31. X. Song, J. Man, S. Song, Z. Wang, State estimation of T-S fuzzy Markovian generalized neural networks with reaction-diffusion terms: a time-varying nonfragile proportional retarded sampled-data control scheme. Neural Comput. Appl. 32, 14639–14653 (2020)

    Article  Google Scholar 

  32. A.M. Stoica, I. Yaesh, Markovian jump delayed Hopfield networks with multiplicative noise. Automatica 44(8), 2157–2162 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  33. W. Tai, A. Zhao, T. Guo, J. Zhou, Energy-to-peak synchronization for uncertain reaction-diffusion delayed neural networks. Phys. Scr. 97, 085207 (2022)

    Article  Google Scholar 

  34. W. Tai, D. Zuo, Z. Xuan, J. Zhou, Z. Wang, Non-fragile \({\cal{L} }_{2}-{\cal{L} }_{\infty }\) filtering for a class of switched neural networks. Math. Comput. Simul. 185, 629–645 (2021)

    Article  MATH  Google Scholar 

  35. Z. Wang, D.W. Ho, X. Liu, State estimation for delayed neural networks. IEEE Trans. Neural Netw. 16(1), 279–284 (2005)

    Article  Google Scholar 

  36. Z. Wang, Y. Liu, X. Liu, State estimation for jumping recurrent neural networks with discrete and distributed delays. Neural Netw. 22(1), 41–48 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  37. M. Wu, Y. He, J. She, Stability Analysis and Robust Control of Time-Delay Systems (Springer, New York, 2010)

    Book  MATH  Google Scholar 

  38. T. Wu, L. Xiong, J. Cao, J.H. Park, J. Cheng, Synchronization of coupled reaction-diffusion stochastic neural networks with time-varying delay via delay-dependent impulsive pinning control algorithm. Commun. Nonlinear Sci. Numer. Simul. 99, 105777 (2021)

    Article  MathSciNet  MATH  Google Scholar 

  39. Y. Xu, F. Sun, W. Li, Exponential synchronization of fractional-order multilayer coupled neural networks with reaction-diffusion terms via intermittent control. Neural Comput. Appl. 33(23), 16019–16032 (2021)

    Article  Google Scholar 

  40. Z. Yan, X. Huang, Y. Fan, J. Xia, H. Shen, Threshold-function-dependent quasi-synchronization of delayed memristive neural networks via hybrid event-triggered control. IEEE Trans. Syst. Man Cybern. 51(11), 6712–6722 (2021)

    Article  Google Scholar 

  41. X. Yang, Q. Song, J. Cao, J. Lu, Synchronization of coupled Markovian reaction-diffusion neural networks with proportional delays via quantized control. IEEE Trans. Neural Netw. Learn. Syst. 30(3), 951–958 (2018)

    Article  MathSciNet  Google Scholar 

  42. H. Yu, Y. He, M. Wu, Delay-dependent state estimation for neural networks with time-varying delay. Neurocomputing 275, 881–887 (2018)

    Article  Google Scholar 

  43. B. Zhang, S. Xu, Y. Zou, Improved delay-dependent exponential stability criteria for discrete-time recurrent neural networks with time-varying delays. Neurocomputing 72(1–3), 321–330 (2008)

    Article  Google Scholar 

  44. R. Zhang, H. Wang, J.H. Park, K. Shi, P. He, Mode-dependent adaptive event-triggered control for stabilization of Markovian memristor-based reaction-diffusion neural networks. IEEE Trans. Neural Netw. Learn. Syst. (2021). https://doi.org/10.1109/TNNLS.2021.3122143

    Article  Google Scholar 

  45. X. Zhang, C. Li, T. Huang, Hybrid impulsive and switching Hopfield neural networks with state-dependent impulses. Neural Netw. 93, 176–184 (2017)

    Article  MATH  Google Scholar 

  46. J. Zhou, Y. Liu, J. Xia, Z. Wang, S. Arik, Resilient fault-tolerant anti-synchronization for stochastic delayed reaction-diffusion neural networks with semi-Markov jump parameters. Neural Netw. 125, 194–204 (2020)

    Article  MATH  Google Scholar 

  47. J. Zhou, S. Xu, B. Zhang, Y. Zou, H. Shen, Robust exponential stability of uncertain stochastic neural networks with distributed delays and reaction-diffusions. IEEE Trans. Neural Netw. Learn. Syst. 23(9), 1407–1416 (2012)

    Article  Google Scholar 

  48. K. Zhou, P.P. Khargonekar, Robust stabilization of linear systems with norm-bounded time-varying uncertainty. Syst. Control Lett. 10(1), 17–20 (1988)

    Article  MathSciNet  MATH  Google Scholar 

  49. Y. Zhou, Y. Liu, J. Zhou, Z. Wang, Quantized passive filtering for switched delayed neural networks. Nonlinear Anal. Model. Control 26(1), 93–112 (2021)

    Article  MathSciNet  MATH  Google Scholar 

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Acknowledgements

This work was supported by the Natural Science Foundation of the Anhui Higher Education Institutions (Grant No. KJ2020A0248).

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Authors and Affiliations

  1. School of Computer Science and Technology, Anhui University of Technology, Ma’anshan, 243032, China

    Weipeng Tai, Tong Guo & Jianping Zhou

  2. Research Institute of Information Technology, Anhui University of Technology, Ma’anshan, 243000, China

    Weipeng Tai & Anqi Zhao

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  1. Weipeng Tai
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Tai, W., Zhao, A., Guo, T. et al. Delay-Independent and Dependent \({\mathcal {L}}_{2}-{\mathcal {L}}_{\infty }\) Filter Design for Time-Delay Reaction–Diffusion Switched Hopfield Networks. Circuits Syst Signal Process 42, 173–198 (2023). https://doi.org/10.1007/s00034-022-02125-0

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