A Review of State Estimation for Time-Delay Neural Networks
DOI:
https://doi.org/10.54097/15gdwg13Keywords:
Time-delay neural networks, state estimation, Lyapunov-Krasovskii functional, integral inequality, switched system, event-triggered mechanismAbstract
In practical engineering, neural networks inevitably suffer from time-delay phenomena caused by signal transmission, hardware response, and data communication. Time-delay will degrade the dynamic performance of neural networks, even lead to oscillation, chaos, and instability. Meanwhile, affected by sensor constraints and external interference, only a small number of system states can be measured directly, which makes state estimation become one of the key technologies in the analysis and application of time-delay neural networks. State estimation refers to reconstructing the real full state of the system through measurable output data, which provides the state basis for stability analysis, fault detection, and feedback control. In recent years, state estimation of time-delay neural networks has become a research hotspot in the fields of control science, intelligent systems, and dynamical systems. This paper systematically summarizes the research results of state estimation for time-delay neural networks. Firstly, the basic model, delay types, and activation function constraints are introduced. Secondly, the core theoretical tools including Lyapunov-Krasovskii functional method, various integral inequalities, reciprocally convex combination lemmas, S-Procedure, and switched system methods are summarized. Thirdly, the research progress of H∞ state estimation, L₂-L∞ state estimation, dissipative state estimation, and event-triggered state estimation is reviewed in detail. Finally, the existing problems and challenges in this field are summarized, and the future development directions including low conservatism, intelligence, network security, and practical application are discussed.
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[1] Wang, Z. D., Liu, Y. R., & Liu, X. H. (2005). H∞ state estimation for discrete-time fuzzy neural networks with time-varying delays. IEEE Transactions on Neural Networks, 16(6), 1609–1621. https://doi.org/10.1109/TNN.2005.852860
[2] Seuret, A., & Gouaisbaut, F. (2013). Wirtinger-based integral inequality: Application to time-delay systems. Automatica, 49(9), 2860–2866. https://doi.org/10.1016/j.automatica.2013.06.013
[3] Gouaisbaut, F., & Seuret, A. (2014). A Bessel-Legendre inequality for time-varying delay systems. Systems & Control Letters, 73, 1–7. https://doi.org/10.1016/j.sysconle.2014.08.002
[4] Park, P. G., Ko, J. W., & Jeong, C. (2011). Reciprocally convex approach to stability of systems with time-varying delays. Automatica, 47(1), 235–238. https://doi.org/10.1016/j.automatica.2010.10.014
[5] Zhang, X. M., & Han, Q. L. (2017). New stability criteria for linear time-delay systems using improved reciprocally convex inequality. IET Control Theory & Applications, 11(10), 1536–1543. https://doi.org/10.1049/iet-cta.2016.1239
[6] Zeng, H. B., He, Y., Wu, M., & Xiao, S. P. (2015). New results on stability analysis for systems with discrete distributed delay. Automatica, 60, 189–192. https://doi.org/10.1016/j.automatica.2015.07.021
[7] Li, J., Zhang, C. K., He, Y., & Zeng, H. B. (2018). Delay-product-type Lyapunov functional for stability analysis of time-varying delay systems. Journal of the Franklin Institute, 355(13), 5602–5619. https://doi.org/10.1016/j.jfranklin.2018.06.021
[8] Wang, Y., Xia, J., Shen, H., & Wang, Z. (2020). Event-triggered H∞ state estimation for delayed neural networks with stochastic cyber-attacks. Applied Mathematics and Computation, 377, 125168. https://doi.org/10.1016/j.amc.2020.125168
[9] Liu, J., Tian, E., Zhang, X., & Xie, X. (2021). Adaptive event-triggered dissipative state estimation for time-delay neural networks. Neurocomputing, 452, 312–321. https://doi.org/10.1016/j.neucom.2021.04.075
[10] Gao, S. J., & Qian, W. (2026). Switched system-based H∞ state estimation for time-varying delay neural networks. IEEE Access, 14, 52103–52112. https://doi.org/10.1109/ACCESS.2026.3582741
[11] Chen, Y., & Wang, L. (2022). L2-L∞ state estimation for generalized neural networks with time-varying delays via improved B-L inequality. Journal of Intelligent & Fuzzy Systems, 43(2), 2451–2460. https://doi.org/10.3233/JIFS-220342
[12] Kim, J. H. (2019). Stability analysis of time-delay systems via negative definite quadratic function method. Automatica, 106, 108–115. https://doi.org/10.1016/j.automatica.2019.04.032
[13] He, Y., Wu, M., & She, J. H. (2006). Delay-dependent stability criteria for linear systems with time-varying delays. IET Control Theory & Applications, 1(1), 43–48. https://doi.org/10.1049/iet-cta:20050062
[14] Zhang, D., & Yu, L. (2012). Passivity and dissipativity analysis for delayed neural networks. Nonlinear Analysis: Real World Applications, 13(3), 1279–1288. https://doi.org/10.1016/j.nonrwa.2011.10.014
[15] Shen, B., Wang, Z., & Liu, X. (2018). Event-triggered state estimation for delayed recurrent neural networks with quantization effects. Neural Computing and Applications, 30(7), 2085–2096. https://doi.org/10.1007/s00521-017-3092-6
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