Search Advanced

AIMS Mathematics

2024, Volume 9, Issue 7: 19049-19067. doi: 10.3934/math.2024927
Previous Article Next Article
Research article

A novel nonzero functional method to extended dissipativity analysis for neural networks with Markovian jumps

  • 1.
    Internet of Things Department, Henan Institute of Economics and Trade, Zhengzhou 450000, China
  • 2.
    College of Automation, Chongqing University, 400044, China
  • 3.
    School of Electrical and Electronic Engineering, Nanyang Technological University, 639798, Singapore
  • 4.
    College of Control Science and Engineering, Zhejiang University, Hangzhou 310058, China
  • Received: 26 March 2024 Revised: 26 May 2024 Accepted: 03 June 2024 Published: 06 June 2024

  • MSC : 37C75, 93C55, 92B20

  • This paper explored the topic of extended dissipativity analysis for Markovian jump neural networks (MJNNs) that were influenced by time-varying delays. A distinctive Lyapunov functional, distinguished by a non-zero delay-product types, was presented. This was achieved by combining a Wirtinger-based double integral inequality with a flexible matrix set. This novel methodology addressed the limitations of the slack matrices found in earlier research. As a result, a fresh condition for extended dissipativity in MJNNs was formulated, utilizing an exponential type reciprocally convex inequality in conjunction with the newly introduced nonzero delay-product types. A numerical example was included to demonstrate the effectiveness of the proposed methodology.

    Citation: Wenlong Xue, Yufeng Tian, Zhenghong Jin. A novel nonzero functional method to extended dissipativity analysis for neural networks with Markovian jumps[J]. AIMS Mathematics, 2024, 9(7): 19049-19067. doi: 10.3934/math.2024927

    Related Papers:

  • This paper explored the topic of extended dissipativity analysis for Markovian jump neural networks (MJNNs) that were influenced by time-varying delays. A distinctive Lyapunov functional, distinguished by a non-zero delay-product types, was presented. This was achieved by combining a Wirtinger-based double integral inequality with a flexible matrix set. This novel methodology addressed the limitations of the slack matrices found in earlier research. As a result, a fresh condition for extended dissipativity in MJNNs was formulated, utilizing an exponential type reciprocally convex inequality in conjunction with the newly introduced nonzero delay-product types. A numerical example was included to demonstrate the effectiveness of the proposed methodology.


    加载中


    [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 Mathematics, 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 Mathematics, 8 (2023), 12472–12485. http://dx.doi.org/10.3934/math.2023626 doi: 10.3934/math.2023626
    [3] J. Geromel, J. da Cruz, On the robustness of optimal regulators for nonlinear discrete-time systems, IEEE T. Automat. Contr., 32 (1987), 703–710. http://dx.doi.org/10.1109/TAC.1987.1104696 doi: 10.1109/TAC.1987.1104696
    [4] A. Seuret, F. Gouaisbaut, Wirtinger-based integral inequality: application to time-delay systems, Automatica, 49 (2013), 2860–2866. http://dx.doi.org/10.1016/j.automatica.2013.05.030 doi: 10.1016/j.automatica.2013.05.030
    [5] M. Park, O. Kwon, J. Park, S. Lee, E. Cha, Stability of time-delay systems via Wirtinger-based double integral inequality, Automatica, 55 (2015), 204–208. http://dx.doi.org/10.1016/j.automatica.2015.03.010 doi: 10.1016/j.automatica.2015.03.010
    [6] 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. http://dx.doi.org/10.1016/j.aml.2023.108764 doi: 10.1016/j.aml.2023.108764
    [7] Z. Wang, S. Ding, Q. Shan, H. Zhang, Stability of recurrent neural networks with time-varying delay via flexible terminal method, IEEE T. Neur. Net. Lear., 28 (2017), 2456–2463. http://dx.doi.org/10.1109/TNNLS.2016.2578309 doi: 10.1109/TNNLS.2016.2578309
    [8] Y. Tian, X. Su, C. Shen, X. Ma, Exponentially extended dissipativity-based filtering of switched neural networks, Automatica, 161 (2024), 111465. http://dx.doi.org/10.1016/j.automatica.2023.111465 doi: 10.1016/j.automatica.2023.111465
    [9] W. Lin, Y. He, C. Zhang, M. Wu, Stability analysis of neural networks with time-varying delay: enhanced stability criteria and conservatism comparison, Commun. Nonlinear Sci., 54 (2018), 118–135. http://dx.doi.org/10.1016/j.cnsns.2017.05.021 doi: 10.1016/j.cnsns.2017.05.021
    [10] C. Zhang, Y. He, L. Jiang, Q. Wang, M.Wu, Stability analysis of discrete-time neural networks with time-varying delay via an extended reciprocally convex matrix inequality, IEEE T. Cybernetics, 47 (2017), 3040–3049. http://dx.doi.org/10.1109/TCYB.2017.2665683 doi: 10.1109/TCYB.2017.2665683
    [11] R. Vadivel, P. Hammachukiattikul, N. Gunasekaran, R. Saravanakumar, H. Dutta, Strict dissipativity synchronization for delayed static neural networks: an event-triggered scheme, Chaos Soliton. Fract., 150 (2021), 111212. http://dx.doi.org/10.1016/j.chaos.2021.111212 doi: 10.1016/j.chaos.2021.111212
    [12] B. Zhang, W. Zheng, S. Xu, Filtering of Markovian jump delay systems based on a new performance index, IEEE T. Circuits-I, 60 (2013), 1250–1263. http://dx.doi.org/10.1109/TCSI.2013.2246213 doi: 10.1109/TCSI.2013.2246213
    [13] S. Shanmugam, R. Vadivel, M. Rhaima, H. Ghoudi, Improved results on an extended dissipative analysis of neural networks with additive time-varying delays using auxiliary function-based integral inequalities, AIMS Mathematics, 8 (2023), 21221–21245. http://dx.doi.org/10.3934/math.20231082 doi: 10.3934/math.20231082
    [14] R. Anbuvithya, S. Dheepika Sri, R. Vadivel, N. Gunasekaran, P. Hammachukiattikul, Extended dissipativity and non-fragile synchronization for recurrent neural networks with multiple time-varying delays via sampled-data control, IEEE Access, 9 (2021), 31454–31466. http://dx.doi.org/10.1109/ACCESS.2021.3060044 doi: 10.1109/ACCESS.2021.3060044
    [15] R. Zhang, D. Zeng, X. Liu, S. Zhong, J. Cheng, New results on stability analysis for delayed Markovian generalized neural networks with partly unknown transition rates, IEEE T. Neur. Net. Lear., 30 (2019), 3384–3395. http://dx.doi.org/10.1109/TNNLS.2019.2891552 doi: 10.1109/TNNLS.2019.2891552
    [16] R. Zhang, D. Zeng, J. Park, Y. Liu, S. Zhong, A new approach to stochastic stability of Markovian neural networks with generalized transition rates, IEEE T. Neur. Net. Lear., 30 (2019), 499–510. http://dx.doi.org/10.1109/TNNLS.2018.2843771 doi: 10.1109/TNNLS.2018.2843771
    [17] W. Lin, Y. He, M. Wu, Q. Liu, Reachable set estimation for Markovian jump neural networks with time-varying delay, Neural Networks, 108 (2018), 527–532. http://dx.doi.org/10.1016/j.neunet.2018.09.011 doi: 10.1016/j.neunet.2018.09.011
    [18] W. Lin, Y. He, C. Zhang, M. Wu, S. 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. http://dx.doi.org/10.1109/TNNLS.2018.2885115 doi: 10.1109/TNNLS.2018.2885115
    [19] 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 (2021), 3240–3246. http://dx.doi.org/10.1109/TNNLS.2020.3008691 doi: 10.1109/TNNLS.2020.3008691
    [20] P. Park, J. Ko, C. Jeong, Reciprocally convex approach to stability of systems with time-varying delays, Automatica, 47 (2011), 235–238. http://dx.doi.org/10.1016/j.automatica.2010.10.014 doi: 10.1016/j.automatica.2010.10.014
    [21] 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. http://dx.doi.org/10.1016/j.automatica.2017.07.056 doi: 10.1016/j.automatica.2017.07.056
    [22] X. Zhang, Q. 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), 222–226. http://dx.doi.org/10.1016/j.automatica.2017.04.048 doi: 10.1016/j.automatica.2017.04.048
    [23] Y. Tian, Z. Wang, Stability analysis and generalized memory controller design for delayed T-S fuzzy systems via flexible polynomial-based functions, IEEE T. Fuzzy Syst., 30 (2022), 728–740. http://dx.doi.org/10.1109/TFUZZ.2020.3046338 doi: 10.1109/TFUZZ.2020.3046338
    [24] V. Yakubovich, The S-procedure in nonlinear control theory, Vestnik Leningrad Univ. Mathe., 4 (1977), 73–93.
    [25] Z. Wang, S. Ding, H. Zhang, Hierarchy of stability criterion for time-delay systems based on multiple integral approach, Appl. Math. Comput., 314 (2017), 422–428. http://dx.doi.org/10.1016/j.amc.2017.07.016 doi: 10.1016/j.amc.2017.07.016
    [26] A. Seuret, F. Gouaisbaut, Stability of linear systems with time-varying delays using Bessel-Legendre inequalities, IEEE T. Automat. Contr., 63 (2018), 225–232. http://dx.doi.org/10.1109/TAC.2017.2730485 doi: 10.1109/TAC.2017.2730485
    [27] R. Vadivel, P. Hammachukiattikul, Q. Zhu, N. Gunasekaran, Event-triggered synchronization for stochastic delayed neural networks: passivity and passification case, Asian J. Control, 25 (2023), 2681–2698. http://dx.doi.org/10.1002/asjc.2965 doi: 10.1002/asjc.2965
    [28] R. Sakthivel, S. Mohanapriya, C. Ahn, P. Selvaraj, State estimation and dissipative-based control design for vehicle lateral dynamics with probabilistic faults, IEEE T. Ind. Electron., 65 (2018), 7193–7201. http://dx.doi.org/10.1109/TIE.2018.2793253 doi: 10.1109/TIE.2018.2793253
    [29] M. Ghorbani, S. Prasad, J. Klauda, B. Brooks, GraphVAMPNet, using graph neural networks and variational approach to Markov processes for dynamical modeling of biomolecules, J. Chem. Phys., 156 (2022), 184103. http://dx.doi.org/10.1063/5.0085607 doi: 10.1063/5.0085607
  • Reader Comments
  • © 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)
通讯作者: 陈斌, bchen63@163.com
  • 1. 

    沈阳化工大学材料科学与工程学院 沈阳 110142

  1. 本站搜索
  2. 百度学术搜索
  3. 万方数据库搜索
  4. CNKI搜索
AIMS Mathematics
1.8 3.4

Metrics

Article views(489) PDF downloads(27) Cited by(0)

Preview PDF
Download XML
Export Citation
Article outline

Figures and Tables

Tables(3)

Other Articles By Authors

Related pages

Tools

/

DownLoad:  Full-Size Img  PowerPoint
Return
Return

Catalog