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AIMS Mathematics

2023, Volume 8, Issue 2: 4973-5006. doi: 10.3934/math.2023249
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Research article

Robust stability and passivity analysis for discrete-time neural networks with mixed time-varying delays via a new summation inequality

  • 1.
    Department of Mathematics, Faculty of Science, Maejo University, Chiang Mai 52290, Thailand
  • 2.
    Department of Mathematics, Faculty of Science, Khon Kaen University, Khon Kaen 40002, Thailand
  • 3.
    Department of Mathematics, Thiruvalluvar University, Vellore 632115, Tamilnadu, India
  • 4.
    Rail System Institute of Rajamangala University of Technology Isan, Nakhon Ratchasima 30000, Thailand
  • Received: 02 September 2022 Revised: 24 November 2022 Accepted: 30 November 2022 Published: 12 December 2022

  • MSC : 37C75, 93C55, 92B20

  • The summation inequality is essential in creating delay-dependent criteria for discrete-time systems with time-varying delays and developing other delay-dependent standards. This paper uses our rebuilt summation inequality to investigate the robust stability analysis issue for discrete-time neural networks that incorporate interval time-varying leakage and discrete and distributed delays. It is a novelty of this study to consider a new inequality, which makes it less conservative than the well-known Jensen inequality, and use it in the context of discrete-time delay systems. Further stability and passivity criteria are obtained in terms of linear matrix inequalities (LMIs) using the Lyapunov-Krasovskii stability theory, coefficient matrix decomposition technique, mobilization of zero equation, mixed model transformation, and reciprocally convex combination. With the assistance of the LMI Control toolbox in Matlab, numerical examples are provided to demonstrate the validity and efficiency of the theoretical findings of this research.

    Citation: Jenjira Thipcha, Presarin Tangsiridamrong, Thongchai Botmart, Boonyachat Meesuptong, M. Syed Ali, Pantiwa Srisilp, Kanit Mukdasai. Robust stability and passivity analysis for discrete-time neural networks with mixed time-varying delays via a new summation inequality[J]. AIMS Mathematics, 2023, 8(2): 4973-5006. doi: 10.3934/math.2023249

    Related Papers:

  • The summation inequality is essential in creating delay-dependent criteria for discrete-time systems with time-varying delays and developing other delay-dependent standards. This paper uses our rebuilt summation inequality to investigate the robust stability analysis issue for discrete-time neural networks that incorporate interval time-varying leakage and discrete and distributed delays. It is a novelty of this study to consider a new inequality, which makes it less conservative than the well-known Jensen inequality, and use it in the context of discrete-time delay systems. Further stability and passivity criteria are obtained in terms of linear matrix inequalities (LMIs) using the Lyapunov-Krasovskii stability theory, coefficient matrix decomposition technique, mobilization of zero equation, mixed model transformation, and reciprocally convex combination. With the assistance of the LMI Control toolbox in Matlab, numerical examples are provided to demonstrate the validity and efficiency of the theoretical findings of this research.


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    [1] S. Arik, Stability analysis of delayed neural networks, IEEE Trans. Circuits Syst., 47 (2000), 1089–1092. http://dx.doi.org/10.1109/81.855465 doi: 10.1109/81.855465
    [2] J. Chen, J. H. Park, S. Xu, Improved stability criteria for discrete-time delayed neural networks via novel Lyapunov-Krasovskii functionals, IEEE Trans. Cybernetics, 52 (2022), 11885–11862. http://dx.doi.org/10.1109/TCYB.2021.3076196 doi: 10.1109/TCYB.2021.3076196
    [3] H. Gao, T. Chen, New results on stability of discrete-time systems with time-varying state delay, IEEE Trans. Automat. Control, 52 (2007), 328–334. https://doi.org/10.1109/TAC.2006.890320 doi: 10.1109/TAC.2006.890320
    [4] H. Gao, T. Chen, T. Chai, Passivity and passification for networked control systems, SIAM J. Control Optim., 46 (2007), 1299–1322. https://doi.org/10.1137/060655110 doi: 10.1137/060655110
    [5] K. Gopalsamy, Stability and oscillations in delay differential equations of population dynamics, Dordrecht: Kluwer Academic Publishers Group, 1992.
    [6] K. Gopalsamy, Leakage delays in BAM, J. Math. Anal., 325 (2007), 1117–1132. https://doi.org/10.1016/j.jmaa.2006.02.039 doi: 10.1016/j.jmaa.2006.02.039
    [7] H. Huang, G. Feng, Improved approach to delay-dependent stability analysis of discrete-time systems with time-varying delay, IET Control Theory Appl., 4 (2010), 2152–2159. http://dx.doi.org/ 10.1049/iet-cta.2009.0225 doi: 10.1049/iet-cta.2009.0225
    [8] L. Jarina Banu, P. Balasubramaniam, K. Patnavelu, Robust stability analysis for discrete-time uncertain neural networks with leakage time-varying delay, Neurocomputing, 151 (2015), 808–816. https://doi.org/10.1016/j.neucom.2014.10.018 doi: 10.1016/j.neucom.2014.10.018
    [9] L. Jin, Y. He, L. Jiang, M. Wu, Extended dissipativity analysis for discrete-time delayed neural networks based on an extended reciprocally convex matrix inequality, Inf. Sci., 462 (2018), 357–366. https://doi.org/10.1016/j.ins.2018.06.037 doi: 10.1016/j.ins.2018.06.037
    [10] L. Jin, Y. He, M. Wu, Improved delay-dependent stability analysis of discrete-time neural networks with time-varying delay, J. Frankl. Inst., 354 (2017), 1922–1936. https://doi.org/10.1016/j.jfranklin.2016.12.027 doi: 10.1016/j.jfranklin.2016.12.027
    [11] O. M. Kwon, S. M. Lee, J. H. Park, E. J. Cha, New approaches on stability criteria or neural networks with interval time-varying delays, Appl. Math. Comput., 218 (2012), 9953–9964. https://doi.org/10.1016/j.amc.2012.03.082 doi: 10.1016/j.amc.2012.03.082
    [12] O. M. Kwon, M. J. Park, J. P. Park, S. M. Lee, E. J. Cha, Improved delay dependent stability criteria for discrete-time systems with time-varying delays, Circuits Syst. Signal Process., 32 (2013), 1949–1962. https://doi.org/10.1007/s00034-012-9543-6 doi: 10.1007/s00034-012-9543-6
    [13] O. M. Kwon, M. J. Park, J. P. Park, S. M. Lee, E. J. Cha, New criteriaon delay-dependent stability for discrete-time neural networks with time-varing delays, Neurocomputing, 121 (2013), 185–194. https://doi.org/10.1016/j.neucom.2013.04.026 doi: 10.1016/j.neucom.2013.04.026
    [14] O. M. Kwon, M. J. Park, J. P. Park, S. M. Lee, E. J. Cha, Stability analysis for discrete–time neural networks with time-varying and stochastic parameter uncertainties, Can. J. Phys., 93 (2015), 398–408. https://doi.org/10.1139/cjp-2014-0264 doi: 10.1139/cjp-2014-0264
    [15] C. Li, T. Huang, On the stability of nonlinear systems with leakage delay, J. Franklin Inst., 346 (2009), 366–377. https://doi.org/10.1016/j.jfranklin.2008.12.001 doi: 10.1016/j.jfranklin.2008.12.001
    [16] C. Li, H. Zhang, X. Liao, Passivity and passification of fuzzy systems with time delays, Comput. Math. Appl., 52 (2006), 1067–1078. https://doi.org/10.1016/j.camwa.2006.03.029 doi: 10.1016/j.camwa.2006.03.029
    [17] T. Li, L. Guo, C. Lin, A new criterion of delay-dependent stability for uncertain time-delay systems, IET Control Theory Appl., 1 (2007), 611–616. http://dx.doi.org/10.1049/iet-cta:20060235 doi: 10.1049/iet-cta:20060235
    [18] X. Li, J. Cao, Delay-dependent stability of neural networks of neutral type with time delay in the leakage term, Nonlinearity, 23 (2010), 1709–1726. http://dx.doi.org/10.1088/0951-7715/23/7/010 doi: 10.1088/0951-7715/23/7/010
    [19] X. D. Li, J. Shen, LMI approach for stationary oscillation of interval neural networks with discrete and distributed time varying delays under impulsive perturbations, IEEE Trans. Neural Networ., 21 (2010), 1555–1563. http://dx.doi.org/10.1109/TNN.2010.2061865 doi: 10.1109/TNN.2010.2061865
    [20] X. Li, X. Fu, P. Balasubramaniam, R. Rakkiyappan, Existence, uniqueness and stability analysis of recurrent neural networks with time delay in the leakage term under impulsive perturbations, Nonlinear Anal.: Real World Appl., 11 (2010), 4092–4108. https://doi.org/10.1016/j.nonrwa.2010.03.014 doi: 10.1016/j.nonrwa.2010.03.014
    [21] X. G. Liu, F. X. Wang, M. L. Tang, Auxiliary function-based summation inequalities and their applications to discrete-time systems, Automatica, 78 (2017), 211–215. https://doi.org/10.1016/j.automatica.2016.12.036 doi: 10.1016/j.automatica.2016.12.036
    [22] Y. Liu, Z. Wang, X. Liu, Asymptotic stability for neural networks with mixed time-delays: the discrete-time case, Neural Networks, 22 (2009), 67–74. https://doi.org/10.1016/j.neunet.2008.10.001 doi: 10.1016/j.neunet.2008.10.001
    [23] Y. Liu, Z. Wang, X. Liu, Global exponential stability of generalized recurrent neural networks with discrete and distributed delays, Neural Networks, 19 (2006), 667–675. https://doi.org/10.1016/j.neunet.2005.03.015 doi: 10.1016/j.neunet.2005.03.015
    [24] S. Mohamad, K. Gopalsamy, Exponential stability of continuous-time and discrete-time cellular neural networks with delays, Appl. Math. Comput., 135 (2003), 17–38. https://doi.org/10.1016/S0096-3003(01)00299-5 doi: 10.1016/S0096-3003(01)00299-5
    [25] P. T. Nam, H. Trinh, P. N. Pathirana, Discrete inequalities based on multiple auxiliary functions and their applications to stability analysis of time-delay systems, J. Frankl. Inst., 352 (2015), 5810–5831. https://doi.org/10.1016/j.jfranklin.2015.09.018 doi: 10.1016/j.jfranklin.2015.09.018
    [26] D. Nishanthi, L. Jarina Banu, P. Balasubramaniam, Robust guaranteed cost state estimation for discrete-time systems with random delays and random uncertainties, Int. J. Adapt. Control Signal Process., 31 (2017), 1361–1372. https://doi.org/10.1002/acs.2770 doi: 10.1002/acs.2770
    [27] P. G. 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
    [28] V. N. Phat, Robust stability and stabilizability of uncertain linear hybrid systems with state delays, IEEE Trans. Circ. Syst., 52 (2005), 94–98. http://dx.doi.org/10.1109/TCSII.2004.840115 doi: 10.1109/TCSII.2004.840115
    [29] K. Ramakrishnan, G. Ray, Robust stability criteria for a class of uncertain discrete-time systems with time-varying delay, Appl. Math. Model., 37 (2013), 1468–1479. https://doi.org/10.1016/j.apm.2012.03.045 doi: 10.1016/j.apm.2012.03.045
    [30] Y. Shan, S. Zhong, J. Cui, L. Hou, Y. Li, Improved criteria of delay-dependent stability for discrete-time neural networks with leakage delay, Neurocomputing, 266 (2017), 409–419. https://doi.org/10.1016/j.neucom.2017.05.053 doi: 10.1016/j.neucom.2017.05.053
    [31] Y. Shu, X. Liu, Y. Liu, Stability and passivity analysis for uncertain discrete-time neural networks with time-varying delay, Neurocomputing, 173 (2016), 1706–1714. https://doi.org/10.1016/j.neucom.2015.09.043 doi: 10.1016/j.neucom.2015.09.043
    [32] Q. Song, J. Liang, Z. Wang, Passivity analysis of discrete-time stochastic neural networks with time-varying delays, Neurocomputing, 72 (2009), 1782–1788. https://doi.org/10.1016/j.neucom.2008.05.006 doi: 10.1016/j.neucom.2008.05.006
    [33] S. K. Tadepalli, V. K. R. Kandanvli, Improved stability results for uncertain discrete-time state-delayed systems in the presence of nonlinearities, Trans. Inst. Meas. Control, 38 (2016), 33–43. http://dx.doi.org/10.1177/0142331214562020 doi: 10.1177/0142331214562020
    [34] Y. Tang, J. Fang, M. Xia, X. Gu, Synchronization of Takagi-Sugeno fuzzy stochastic discrete-time complex networks with mixed time-varying delays, Appl. Math. Model., 34 (2010), 843–855. https://doi.org/10.1016/j.apm.2009.07.015 doi: 10.1016/j.apm.2009.07.015
    [35] J. Tian, S. Zhong, Improved delay-dependent stability criterion for neural networks with time-varying delay, Appl. Math. Comput., 217 (2011), 10278–10288. https://doi.org/10.1016/j.amc.2011.05.029 doi: 10.1016/j.amc.2011.05.029
    [36] S. Udpin, P. Niamsup, Robust stability of discrete-time LPD neural networks with time-varying delay, Commun. Nonlinear Sci. Numer. Simul., 14 (2009), 3914–3924. https://doi.org/10.1016/j.cnsns.2008.08.018 doi: 10.1016/j.cnsns.2008.08.018
    [37] X. Wan, M. Wu, Y. He, J. She, Stability analysis for discrete time-delay systems based on new finite-sum inequalities, Inf. Sci., 369 (2016), 119–127. https://doi.org/10.1016/j.ins.2016.06.024 doi: 10.1016/j.ins.2016.06.024
    [38] T. Wang, M. X. Xue, C. Zhang, S. M. Fei, Improved stability criteria on discrete-time systems with time-varying and distributed delays, Int. J. Autom. Comput., 10 (2013), 260–266. https://doi.org/10.1007/s11633-013-0719-8 doi: 10.1007/s11633-013-0719-8
    [39] Z. Wang, Y. Liu, X. Liu, On global asymptotic stability of neural networks with discrete and distributed delays, Phys. Lett. A, 345 (2005), 299–308. https://doi.org/10.1016/j.physleta.2005.07.025 doi: 10.1016/j.physleta.2005.07.025
    [40] T. Wang, C. Zhang, S. Fei, T. Li, Further stability criteria on discrete-time delayed neural networks with distributed delay, Neurocomputing, 111 (2013), 195–203. https://doi.org/10.1016/j.neucom.2012.12.017 doi: 10.1016/j.neucom.2012.12.017
    [41] L. Wu, W. Zheng, Passivity-based sliding mode control of uncertain singular time-delay systems, Automatica, 45 (2009), 2120–2127. https://doi.org/10.1016/j.automatica.2009.05.014 doi: 10.1016/j.automatica.2009.05.014
    [42] M. Wu, C. Peng, J. Zhang, M. Fei, Y. Tian, Further results on delay-dependent stability criteria of discrete systems with an interval time-varying delay, J. Franklin Inst., 354 (2017), 4955–4965. https://doi.org/10.1016/j.jfranklin.2017.05.005 doi: 10.1016/j.jfranklin.2017.05.005
    [43] L. Xie, M. Fu, H. Li, Passivity analysis and passification for uncertain signal processing systems, IEEE Trans. Signal Process., 46 (1998), 2394–2403. http://dx.doi.org/10.1109/78.709527 doi: 10.1109/78.709527
    [44] C. K. Zhang, Y. He, L. Jiang, M. Wu, An improved summation inequality to discrete-time systems with time-varying delay, Automatica, 74 (2016), 10–15. https://doi.org/10.1016/j.automatica.2016.07.040 doi: 10.1016/j.automatica.2016.07.040
    [45] X. M. Zhang, Q. L. Han, X. Ge, B. L. Zhang, Delay-variation-dependent criteria on extended dissipativity for discrete-time neural networks with time-varying delay, IEEE Trans. Neur. Net. Lear., 2021, 1–10. http://dx.doi.org/10.1109/TNNLS.2021.3105591
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