Stability analysis of delayed neural networks via compound-parameter -based integral inequality

Wenlong Xue; Zhenghong Jin; Yufeng Tian; Wenlong Xue; Zhenghong Jin; Yufeng Tian

doi:10.3934/math.2024942

AIMS Mathematics

2024, Volume 9, Issue 7: 19345-19360. doi: 10.3934/math.2024942

Previous Article Next Article

Research article

Stability analysis of delayed neural networks via compound-parameter -based integral inequality

1.
Internet of Things Department, Henan Institute of Economics and Trade, Zhengzhou 450000, China
2.
College of Control Science and Engineering, Zhejiang University, Hangzhou, 310058, China
3.
School of Electrical and Electronic Engineering, Nanyang Technological University, 639798, Singapore
4.
College of Automation, Chongqing University, 400044, China

Received: 18 March 2024 Revised: 28 May 2024 Accepted: 03 June 2024 Published: 11 June 2024
MSC : 37C75, 93C55, 92B20

This paper revisits the issue of stability analysis of neural networks subjected to time-varying delays. A novel approach, termed a compound-matrix-based integral inequality (CPBII), which accounts for delay derivatives using two adjustable parameters, is introduced. By appropriately adjusting these parameters, the CPBII efficiently incorporates coupling information along with delay derivatives within integral inequalities. By using CPBII, a novel stability criterion is established for neural networks with time-varying delays. The effectiveness of this approach is demonstrated through a numerical illustration.
- neural networks,
- time-varying delay,
- stability analysis,
- integral inequality,
- delay derivative
Citation: Wenlong Xue, Zhenghong Jin, Yufeng Tian. Stability analysis of delayed neural networks via compound-parameter -based integral inequality[J]. AIMS Mathematics, 2024, 9(7): 19345-19360. doi: 10.3934/math.2024942

Related Papers:

Abstract

This paper revisits the issue of stability analysis of neural networks subjected to time-varying delays. A novel approach, termed a compound-matrix-based integral inequality (CPBII), which accounts for delay derivatives using two adjustable parameters, is introduced. By appropriately adjusting these parameters, the CPBII efficiently incorporates coupling information along with delay derivatives within integral inequalities. By using CPBII, a novel stability criterion is established for neural networks with time-varying delays. The effectiveness of this approach is demonstrated through a numerical illustration.

References

[1]	N. Huo, B. Li, Y. Li, Global exponential stability and existence of almost periodic solutions in distribution for Clifford-valued stochastic high-order Hopfield neural networks with time-varying delays, AIMS Math., 7 (2022), 3653–3679. http://dx.doi.org/10.3934/math.2022202 doi: 10.3934/math.2022202
[2]	H. Qiu, L. Wan, Z. Zhou, Q. Zhang, Q. Zhou, Global exponential periodicity of nonlinear neural networks with multiple time-varying delays, AIMS Math., 8 (2023), 12472–12485. http://dx.doi.org/10.3934/math.2023626 doi: 10.3934/math.2023626
[3]	R. Wei, J. Cao, W. Qian, C. Xue, X. Ding, Finite-time and fixed-time stabilization of inertial memristive Cohen-Grossberg neural networks via non-reduced order method, AIMS Math., 6 (2021), 6915–6932. http://dx.doi.org/10.3934/math.2021405 doi: 10.3934/math.2021405
[4]	J. Kim, Further improvement of Jensen inequality and application to stability of time-delayed systems, Automatica, 64 (2016), 121–125. https://doi.org/10.1016/j.automatica.2015.08.025 doi: 10.1016/j.automatica.2015.08.025
[5]	O. M. Kwon, M. J. Park, S. M. Lee, J. H. Park, E. J. Cha, Stability for neural networks with time-varying delays via some new approaches, IEEE T. Neur. Net. Lear., 24 (2013), 181–193. https://doi.org/10.1109/TNNLS.2012.2224883 doi: 10.1109/TNNLS.2012.2224883
[6]	X. M. Zhang, Q. L. Han, Z. Zeng, Hierarchical type stability criteria for delayed neural networks via canonical Bessel-Legendre inequalities, IEEE T. Cybern., 48 (2018), 1660–1671. https://doi.org/10.1109/TCYB.2017.2776283 doi: 10.1109/TCYB.2017.2776283
[7]	T. Wu, S. Gorbachev, H. Lam, J. Park, L. Xiong, J. Cao, Adaptive event-triggered space-time sampled-data synchronization for fuzzy coupled RDNNs under hybrid random cyberattacks, IEEE T. Fuzzy Syst., 31 (2023), 1855–1869. https://doi.org/10.1109/TFUZZ.2022.3215747 doi: 10.1109/TFUZZ.2022.3215747
[8]	T. Wu, J. Cao, J. Park, K. Shi, L. Xiong, T. Huang, Attack-resilient dynamic event-triggered synchronization of fuzzy reaction-diffusion dynamic networks with multiple cyberattacks, IEEE T. Fuzzy Syst., 32 (2024), 498–509. https://doi.org/10.1109/TFUZZ.2023.3300882 doi: 10.1109/TFUZZ.2023.3300882
[9]	T. Wu, J. Cao, L. Xiong, J. Park, X. Tan, Adaptive event-triggered mechanism to synchronization of reaction-diffusion CVNNs and its application in image secure communication, IEEE T. Syst. Man Cy-S., 53 (2023), 5307–5320. https://doi.org/10.1109/TSMC.2023.3258222 doi: 10.1109/TSMC.2023.3258222
[10]	C. K. Zhang, Y. He, L. Jiang, M. Wu, Notes on stability of time-delay systems: Bounding inequalities and augmented Lyapunov-Krasovskii functionals, IEEE T. Autom. Control, 62 (2017), 5331–5336. https://doi.org/10.1109/TAC.2016.2635381 doi: 10.1109/TAC.2016.2635381
[11]	W. Lin, Y. He, C. Zhang, M. Wu, J. Shen, Extended dissipativity analysis for Markovian jump neural networks with time-varying delay via delay-product-type functionals, IEEE T. Neur. Net. Lear., 30 (2019), 2528–2537. https://doi.org/10.1109/TNNLS.2018.2885115 doi: 10.1109/TNNLS.2018.2885115
[12]	Y. Tian, Z. Wang, Extended dissipativity analysis for Markovian jump neural networks via double-integral-based delay-product-type Lyapunov functional, IEEE T. Neur. Net. Lear., 32 (2020), 3240–3246. https://doi.org/10.1109/TNNLS.2020.3008691 doi: 10.1109/TNNLS.2020.3008691
[13]	K. Gu, V. L. Kharitonov, J. Chen, Stability of Time-Delay Systems, 2003.
[14]	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
[15]	H.B. Zeng, Y. He, M. Wu, J. She, Free-matrix-based integral inequality for stability analysis of systems with time-varying delay, IEEE T. Autom. Control, 60 (2015), 2768–2772. https://doi.org/10.1109/TAC.2015.2404271 doi: 10.1109/TAC.2015.2404271
[16]	H.B. Zeng, Y. He, M. Mu, J. She, New results on stability analysis for systems with discrete distributed delay, Automatica, 60 (2015), 189–192. https://doi.org/10.1016/j.automatica.2015.07.017 doi: 10.1016/j.automatica.2015.07.017
[17]	X. M. Zhang, W. J. Lin, Q. L. Han, Y. He, M. Wu, Global asymptotic stability for delayed neural networks using an integral inequality based on nonorthogonal polynomials, IEEE T. Neur. Net. Lear., 29 (2018), 4487–4493. https://doi.org/10.1109/TNNLS.2017.2750708 doi: 10.1109/TNNLS.2017.2750708
[18]	J. Chen, S. Xu, B. Zhang, Single/Multiple integral inequalities with applications to stability analysis of time-delay systems, IEEE T. Autom. Control, 62 (2017), 3488–3493. https://doi.org/10.1109/TAC.2016.2617739 doi: 10.1109/TAC.2016.2617739
[19]	C. K. Zhang, Y. He, L. Jiang, W. J. Lin, M. Wu, Delay-dependent stability analysis of neural networks with time-varying delay: A generalized free-weighting-matrix approach, Appl. Math. Comput., 294 (2017), 102–120. https://doi.org/10.1016/j.amc.2016.08.043 doi: 10.1016/j.amc.2016.08.043
[20]	A. Seuret, F. Gouaisbaut, Hierarchy of LMI conditions for the stability analysis of time-delay systems, Syst. Control Lett., 81 (2015), 1–8. https://doi.org/10.1016/j.sysconle.2015.03.007 doi: 10.1016/j.sysconle.2015.03.007
[21]	A. Seuret, F. Gouaisbaut, Stability of linear systems with time-varying delays using Bessel-Legendre inequalities, IEEE T. Autom. Control, 63 (2018), 225–232. https://doi.org/10.1109/TAC.2017.2730485 doi: 10.1109/TAC.2017.2730485
[22]	Y. Huang, Y. He, J. An, M. Wu, Polynomial-type Lyapunov-Krasovskii functional and Jacobi-Bessel inequality: Further results on stability analysis of time-delay systems, IEEE Trans. Autom. Control, 66 (2021), 2905–2912. https://doi.org/10.1109/TAC.2020.3013930 doi: 10.1109/TAC.2020.3013930
[23]	P. Park, J. W. Ko, C. Jeong, Reciprocally convex approach to stability of systems with time-varying delays, Automatica, 47 (2011), 235–238. https://doi.org/10.1016/j.automatica.2010.10.014 doi: 10.1016/j.automatica.2010.10.014
[24]	X. M. Zhang, Q. L. Han, A. Seuret, F. Gouaisbaut, An improved reciprocally convex inequality and an augmented Lyapunov-Krasovskii functional for stability of linear systems with time-varying delay, Automatica, 84 (2017), 221–226. https://doi.org/10.1016/j.automatica.2017.04.048 doi: 10.1016/j.automatica.2017.04.048
[25]	C. Zhang, Y. He, L. Jiang, M. Wu, Q. Wang, An extended reciprocally convex matrix inequality for stability analysis of systems with time-varying delay, Automatica, 85 (2017), 481–485. https://doi.org/10.1016/j.automatica.2017.07.056 doi: 10.1016/j.automatica.2017.07.056
[26]	W. I. Lee, S. Y. Lee, P. G. Park, Affine Bessel-Legendre inequality: Application to stability analysis for systems with time-varying delays, Automatica, 93 (2018), 535–539. https://doi.org/10.1016/j.automatica.2018.03.073 doi: 10.1016/j.automatica.2018.03.073
[27]	J. Chen, J. H. Park, S. Xu, Stability analysis for delayed neural networks with an improved general free-matrix-based integral inequality, IEEE T. Neur. Net. Lear. Syst., 31 (2020), 675–684. https://doi.org/10.1109/TNNLS.2019.2909350 doi: 10.1109/TNNLS.2019.2909350
[28]	Y. Tian, Y. Yang, X. Ma, X. Su, Stability of discrete-time delayed systems via convex function-based summation inequality, Appl. Math. Lett., 145 (2023), 108764, https://doi.org/10.1016/j.aml.2023.108764 doi: 10.1016/j.aml.2023.108764

Reader Comments

Your name:*

Email:*
© 2024 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)