Memory-based switched event-triggered stabilization with switched gains for memristive neural networks

Tianran Bu; Tianran Bu

doi:10.3934/era.2026234

Electronic Research Archive

2026, Volume 34, Issue 8: 5267-5285. doi: 10.3934/era.2026234

Previous Article Next Article

Research article

Memory-based switched event-triggered stabilization with switched gains for memristive neural networks

Tianran Bu ^,

School of Information and Artificial Intelligence, Anhui Business College, Wuhu 241002, China

Received: 14 April 2026 Revised: 03 May 2026 Accepted: 18 May 2026 Published: 22 June 2026

This paper investigates the problem of event-triggered stabilization for memristive neural networks (MNNs). To reduce the consumption of limited network communication resources, a memory-based switched event-triggered rule is proposed, in which an integral-type time-memory function is incorporated into the triggering threshold to characterize the average historical state information. The proposed event-triggered rule divides the entire time interval into a variable-length waiting interval and a continuous, event-triggered interval. To enlarge the maximum allowable variable-length waiting interval, a switched controller with different feedback gains is designed for these two intervals. A sufficient condition ensuring asymptotic stability of the closed-loop MNN is derived by constructing a piecewise Lyapunov functional, employing several integral inequalities, and introducing appropriate slack matrices. Subsequently, by decoupling the nonlinearities, a convex matrix-inequalities-based condition is established, enabling the explicit computation of the feedback gains. Finally, a simulation example is provided to demonstrate the effectiveness of the proposed memory-based switched event-triggered stabilization scheme.
- memristive neural network,
- switched gain,
- asymptotic stability,
- event-triggered control
Citation: Tianran Bu. Memory-based switched event-triggered stabilization with switched gains for memristive neural networks[J]. Electronic Research Archive, 2026, 34(8): 5267-5285. doi: 10.3934/era.2026234

Related Papers:

Abstract

This paper investigates the problem of event-triggered stabilization for memristive neural networks (MNNs). To reduce the consumption of limited network communication resources, a memory-based switched event-triggered rule is proposed, in which an integral-type time-memory function is incorporated into the triggering threshold to characterize the average historical state information. The proposed event-triggered rule divides the entire time interval into a variable-length waiting interval and a continuous, event-triggered interval. To enlarge the maximum allowable variable-length waiting interval, a switched controller with different feedback gains is designed for these two intervals. A sufficient condition ensuring asymptotic stability of the closed-loop MNN is derived by constructing a piecewise Lyapunov functional, employing several integral inequalities, and introducing appropriate slack matrices. Subsequently, by decoupling the nonlinearities, a convex matrix-inequalities-based condition is established, enabling the explicit computation of the feedback gains. Finally, a simulation example is provided to demonstrate the effectiveness of the proposed memory-based switched event-triggered stabilization scheme.

References

[1]	L. Chua, Memristor-the missing circuit element, IEEE Trans. Circuit Theory, 18 (1971), 507–519. https://doi.org/10.1109/TCT.1971.1083337 doi: 10.1109/TCT.1971.1083337
[2]	D. B. Strukov, G. S. Snider, D. R. Stewart, R. S. Williams, The missing memristor found, Nature, 453 (2008), 80–83. https://doi.org/10.1038/nature06932 doi: 10.1038/nature06932
[3]	E. Arslan, G. Narayanan, M. S. Ali, S. Arik, S. Saroha, Controller design for finite-time and fixed-time stabilization of fractional-order memristive complex-valued bam neural networks with uncertain parameters and time-varying delays, Neural Networks, 130 (2020), 60–74. https://doi.org/10.1016/j.neunet.2020.06.021 doi: 10.1016/j.neunet.2020.06.021
[4]	Y. Sheng, T. Huang, Z. Zeng, Exponential stabilization of fuzzy memristive neural networks with multiple time delays via intermittent control, IEEE Trans. Syst. Man Cybern. Syst., 52 (2022), 3092–3101. https://doi.org/10.1109/TSMC.2021.3062381 doi: 10.1109/TSMC.2021.3062381
[5]	S. Zhang, M. Tang, X. Liu, X. Zhang, Mittag-Lefflerstability and stabilization of delayed fractional-order memristive neural networks based on a new Razumikhin-type theorem, J. Franklin Inst., 361 (2024), 1211–1226. https://doi.org/10.1016/j.jfranklin.2024.01.008 doi: 10.1016/j.jfranklin.2024.01.008
[6]	H. Liu, J. Cheng, J. Cao, I. Katib, Preassigned-time synchronization for complex-valued memristive neural networks with reaction-diffusion terms and Markov parameters, Neural Networks, 169 (2024), 520–531. https://doi.org/10.1016/j.neunet.2023.11.011 doi: 10.1016/j.neunet.2023.11.011
[7]	R. Suvetha, Y. Ma, P. Prakash, Fault tolerant control design for memristive bidirectional associative memory neural networks and its application in genetic regulatory networks, Neural Comput. Appl., 38 (2026), 136. https://doi.org/10.1007/s00521-025-11811-4 doi: 10.1007/s00521-025-11811-4
[8]	N. Liu, J. Cheng, Y. Chen, H. Yan, D. Zhang, W. Qi, Adaptive protocol-based control for reaction-diffusion memristive neural networks with semi-Markov switching parameters, Inf. Sci., 677 (2024), 120947. https://doi.org/10.1016/j.ins.2024.120947 doi: 10.1016/j.ins.2024.120947
[9]	S. Xiao, Z. Wang, X. Si, G. Liu, Mean-square exponential stabilization of memristive neural networks: Dealing with replay attacks and communication interruptions, Commun. Nonlinear Sci. Numer. Simul., 138 (2024), 108188. https://doi.org/10.1016/j.cnsns.2024.108188 doi: 10.1016/j.cnsns.2024.108188
[10]	Y. Zhang, F. Kong, Q. Zhu, T. Huang, Quantized control based on stabilization of discontinuous memristor-based fuzzy inertial neural networks with proportional delays, IEEE Trans. Syst. Man Cybern. Syst., 54 (2024), 5756–5767. https://doi.org/10.1109/TSMC.2024.3408469 doi: 10.1109/TSMC.2024.3408469
[11]	X. Zhang, Q. Han, X. Ge, D. Ding, L. Ding, D. Yue, et al., Networked control systems: A survey of trends and techniques, IEEE/CAA J. Autom. Sin., 7 (2020), 1–17. https://doi.org/10.1109/JAS.2019.1911651 doi: 10.1109/JAS.2019.1911651
[12]	Y. Wang, S. Wu, C. Lei, J. Jiao, Q. Zhang, A review on wireless networked control system: The communication perspective, IEEE Internet Things J., 11 (2024), 7499–7524. https://doi.org/10.1109/JIOT.2023.3342032 doi: 10.1109/JIOT.2023.3342032
[13]	K. Liu, E. Fridman, Y. Xia, Networked Control Under Communication Constraints: A Time-Delay Approach, $1^{st}$ edition, Springer, 2020. https://doi.org/10.1007/978-981-15-4230-5
[14]	P. Tabuada, Event-triggered real-time scheduling of stabilizing control tasks, IEEE Trans. Autom. Control, 52 (2007), 1680–1685. https://doi.org/10.1109/TAC.2007.904277 doi: 10.1109/TAC.2007.904277
[15]	L. Zhang, S. Xu, Static pinning synchronization control of self-triggered coupling dynamical networks, Neural Networks, 182 (2025), 106798. https://doi.org/10.1016/j.neunet.2024.106798 doi: 10.1016/j.neunet.2024.106798
[16]	B. Jiang, J. Wei, Y. Liu, W. Gui, Periodic event-triggered impulsive control of linear uncertain systems, IEEE Trans. Autom. Sci. Eng., 22 (2024), 6876–6883. https://doi.org/10.1109/TASE.2024.3456125 doi: 10.1109/TASE.2024.3456125
[17]	W. Wu, L. He, Z. Yan, J. Zhou, Event-triggered extended dissipativity stabilization of semi-Markov switching systems, Appl. Math. Modell., 118 (2023), 618–640. https://doi.org/10.1016/j.apm.2023.01.045 doi: 10.1016/j.apm.2023.01.045
[18]	X. Chen, S. Hu, T. Yang, X. Xie, J. Qiu, Event-triggered bipartite consensus of multiagent systems with input saturation and DoS attacks over weighted directed networks, IEEE Trans. Syst. Man Cybern. Syst., 54 (2024), 4054–4065. https://doi.org/10.1109/TSMC.2024.3377213 doi: 10.1109/TSMC.2024.3377213
[19]	C. Yi, J. Cai, R. Guo, Synchronization of a class of nonlinear multiple neural networks with delays via a dynamic event-triggered impulsive control strategy, Electron. Res. Arch., 32 (2024), 4581–4603. https://doi.org/10.3934/era.2024208 doi: 10.3934/era.2024208
[20]	Y. Wang, H. Tuo, H. Lyu, Z. Cheng, Y. Xin, Aperiodic switching event-triggered stabilization of continuous memristive neural networks with interval delays, Neural Networks, 164 (2023), 264–274. https://doi.org/10.1016/j.neunet.2023.04.036 doi: 10.1016/j.neunet.2023.04.036
[21]	Z. Yan, X. Huang, J. Cao, Variable-sampling-period dependent global stabilization of delayed memristive neural networks based on refined switching event-triggered control, Sci. China Inf. Sci., 63 (2020), 212201. https://doi.org/10.1007/s11432-019-2664-7 doi: 10.1007/s11432-019-2664-7
[22]	Z. Fei, C. Guan, H. Gao, Exponential synchronization of networked chaotic delayed neural network by a hybrid event trigger scheme, IEEE Trans. Neural Networks Learn. Syst., 29 (2018), 2558–2567. https://doi.org/10.1109/TNNLS.2017.2700321 doi: 10.1109/TNNLS.2017.2700321
[23]	A. Selivanov E. Fridman, Event-triggered $H_{\infty}$ control: A switching approach, IEEE Trans. Autom. Control, 61 (2016), 3221–3226. https://doi.org/10.1109/TAC.2015.2508286 doi: 10.1109/TAC.2015.2508286
[24]	J. Zhou, J. Dong, S. Xu, C. K. Ahn, Input-to-state stabilization for Markov jump systems with dynamic quantization and multimode injection attacks, IEEE Trans. Syst. Man Cybern. Syst., 54 (2024), 2517–2529. https://doi.org/10.1109/TSMC.2023.3344869 doi: 10.1109/TSMC.2023.3344869
[25]	Y. Liu, P. Zhang, S. Lee, X. Xie, Observer-based adaptive event-triggered control for interval type-2 fuzzy systems under multiple cyber-attacks, IEEE Trans. Fuzzy Syst., 32 (2024), 2438–2447. https://doi.org/10.1109/TFUZZ.2024.3354241 doi: 10.1109/TFUZZ.2024.3354241
[26]	Y. Zhou, X. Chang, J. H. Park, Quantized asynchronous filtering for fuzzy semi-Markov switching systems with multiple stochastic delays under deception attacks, IEEE Trans. Fuzzy Syst., 32 (2024), 2378–2389. https://doi.org/10.1109/TFUZZ.2023.3346927 doi: 10.1109/TFUZZ.2023.3346927
[27]	N. Ayyappan, N. Gunasekaran, A. Manivannan, S. Lakshmanan, Finite-time $H_\infty$ boundedness of delayed interconnected systems using sliding mode control with partitioned interval strategy, Commun. Nonlinear Sci. Numer. Simul., 157 (2026), 109673. https://doi.org/10.1016/j.cnsns.2026.109673 doi: 10.1016/j.cnsns.2026.109673
[28]	Y. Chen, X. Zhang, Z. Yan, O. Faydasicok, S. Arik, Sampled-data control for Markovian switching neural networks with output quantization and packet dropouts, J. Franklin Inst., 361 (2024), 107252. https://doi.org/10.1016/j.jfranklin.2024.107252 doi: 10.1016/j.jfranklin.2024.107252
[29]	Q. Song, Q. Wu, Y. Liu, Stabilization of chaotic quaternion-valued neutral-type neural networks via sampled-data control with two-sided looped functional approach, Nonlinear Anal. Modell. Control, 29 (2024), 1150–1166. https://doi.org/10.15388/namc.2024.29.37852 doi: 10.15388/namc.2024.29.37852
[30]	G. Jiang, L. Wang, X. Zong, Q. Xiao, G. Zhang, J. Hu, Practically predefined-time stabilization of stochastic fuzzy memristive neural networks under deception attacks, IEEE Trans. Cybern., 56 (2026), 1071–1082. https://doi.org/10.1109/TCYB.2025.3621274 doi: 10.1109/TCYB.2025.3621274
[31]	Y. Ni, Z. Wang, Y. Fan, X. Huang, H. Shen, Memory-based event-triggered control for global synchronization of chaotic Lur'e systems and its application, IEEE Trans. Syst. Man Cybern. Syst., 53 (2023), 1920–1931. https://doi.org/10.1109/TSMC.2022.3207353 doi: 10.1109/TSMC.2022.3207353
[32]	Y. Liu, G. Cui, G. Gao, Event-triggered synchronization control for neural networks against DoS attacks, Electron. Res. Arch., 33 (2025), 121–141. https://doi.org/10.3934/era.2025007 doi: 10.3934/era.2025007
[33]	Y. Liu, Z. Fang, J. H. Park, F. Fang, Quantized event-triggered synchronization of discrete-time chaotic neural networks with stochastic deception attack, IEEE Trans. Syst. Man Cybern. Syst., 53 (2023), 4511–4521. https://doi.org/10.1109/TSMC.2023.3251355 doi: 10.1109/TSMC.2023.3251355
[34]	J. Zhou, X. Ma, Z. Yan, S. Arik, Non-fragile output-feedback control for time-delay neural networks with persistent dwell time switching: A system mode and time scheduler dual-dependent design, Neural Networks, 169 (2024), 733–743. https://doi.org/10.1016/j.neunet.2023.11.007 doi: 10.1016/j.neunet.2023.11.007
[35]	T. Bu, Quantized $H_\infty$ synchronization for Hopfield networks subject to time-variable delay, Networks Heterogen. Media, 20 (2025), 1392–1410. https://doi.org/10.3934/nhm.2025060 doi: 10.3934/nhm.2025060
[36]	Z. Yan, X. Huang, J. Liang, Aperiodic sampled-data control for stabilization of memristive neural networks with actuator saturation: A dynamic partitioning method, IEEE Trans. Cybern., 53 (2023), 1725–1737. https://doi.org/10.1109/TCYB.2021.3108805 doi: 10.1109/TCYB.2021.3108805
[37]	C. Ge, X. Liu, Y. Liu, C. Hua, Event-triggered exponential synchronization of the switched neural networks with frequent asynchronism, IEEE Trans. Neural Networks Learn. Syst., 35 (2024), 1750–1760. https://doi.org/10.1109/TNNLS.2022.3185098 doi: 10.1109/TNNLS.2022.3185098
[38]	Y. Liu, Z. Wang, X. Huang, H. Shen, Multisynchronization of coupled multistable neural networks via event-triggered impulsive control and its application to associative memory, IEEE Trans. Autom. Sci. Eng., 22 (2025), 6729–6739. https://doi.org/10.1109/TASE.2024.3453294 doi: 10.1109/TASE.2024.3453294
[39]	K. Gu, V. L. Kharitonov, J. Chen, Stability of Time-Delay Systems, $1^{st}$ edition, Birkhäuser, 2003. https://doi.org/10.1007/978-1-4612-0039-0
[40]	A. Seuret, F. Gouaisbaut, Wirtinger-based integral inequality: Application to time-delay systems, Automatica, 49 (2013), 2860–2866. https://doi.org/10.1016/j.automatica.2013.05.030 doi: 10.1016/j.automatica.2013.05.030

Reader Comments

Your name:*

Email:*
© 2026 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)