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AIMS Mathematics

2024, Volume 9, Issue 7: 19049-19067. doi: 10.3934/math.2024927
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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.


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    [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
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