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doi: 10.3934/dcdss.2022081
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Novel criteria for robust stability of Cohen-Grossberg neural networks with multiple time delays

1. 

Istanbul University, Faculty of Science, Department of Mathematics 34134 Vezneciler, Istanbul, Turkey

2. 

Istanbul University-Cerrahpasa, Faculty of Engineering, Department of Computer Engineering 34320 Avcilar, Istanbul, Turkey

* Corresponding author: Ozlem Faydasicok

Received  January 2022 Revised  February 2022 Early access March 2022

Fund Project: Sabri Arik is supported by Scientific Research Projects Coordination Unit of Istanbul University-Cerrahpasa. Project number: BYP-2020-34652

This research paper deals with the investigation of global robust stability results for Cohen-Grossberg neural networks involving the multiple constant time delays. The activation functions in this neural network model are supposed to be in the set of non-decreasing slope-bounded nonlinear functions and the uncertainties in the constant network parameters are considered to have bounded upper norms. By employing a proper positive definite Lyapunov-type functional and using homeomorphism mapping theory, we propose some novel sets of novel conditions that assure both existence, uniqueness and global robust asymptotic stability of equilibrium points of this nonlinear Cohen-Grossberg-type neural network model involving the multiple time delays. The derived robustly stable conditions mainly rely on examining some proper relationships that are imposed on constant valued interconnection matrices of this delayed neural network. These stability conditions can be certainly verified by employing various simple and useful properties of real interval matrices. Some comparisons are made to address the key advantages of these novel criteria over previously reported corresponding results. An instructive example is also examined to observe novelty of these proposed criteria.

Citation: Muhammet Mert Ketencigil, Ozlem Faydasicok, Sabri Arik. Novel criteria for robust stability of Cohen-Grossberg neural networks with multiple time delays. Discrete and Continuous Dynamical Systems - S, doi: 10.3934/dcdss.2022081
References:
[1]

S. Arik, New criteria for global robust stability of delayed neural networks with norm-bounded uncertainties, IEEE Transactions on Neural Networks and Learning Systems, 25 (2014), 1045-1052. 

[2]

S. Arik, Further analysis of stability of uncertain neural networks with multiple time delays, Adv. Difference Equ., 2014 (2014), 41, 16 pp. doi: 10.1186/1687-1847-2014-41.

[3]

S. Arik, Dynamical analysis of uncertain neural networks with multiple time delays, Internat. J. Systems Sci., 47 (2016), 730-739.  doi: 10.1080/00207721.2014.902158.

[4]

E. Arslan, Novel criteria for global robust stability of dynamical neural networks with multiple time delays, Neural Networks, 142 (2021), 119-127.  doi: 10.1016/j.neunet.2021.04.039.

[5]

Y. CaoR. SriramanN. Shyamsundarraj and R. Samidurai, Robust stability of uncertain stochastic complex-valued neural networks with additive time-varying delays, Math. Comput. Simulation, 171 (2020), 207-220.  doi: 10.1016/j.matcom.2019.05.011.

[6]

J. ChenB. Chen and Z. Zeng, Basic theorem and global exponential stability of differential algebraic neural networks with delay, Neural Networks, 140 (2021), 336-343.  doi: 10.1016/j.neunet.2021.01.017.

[7]

S. ChenQ. SongZ. ZhaoY. Liu and F. E. Alsaadi, Global asymptotic stability of fractional-order complex-valued neural networks with probabilistic time-varying delays, Neurocomputing, 450 (2021), 311-318.  doi: 10.1016/j.neucom.2021.04.043.

[8]

T. Chen and L. Rong, Robust global exponential stability of Cohen-Grossberg neural networks with time delays, IEEE Transactions on Neural Networks, 15 (2004), 203-206. 

[9]

Y. ChenZ. WangY. Liu and F. E. Alsaadi, Stochastic stability for distributed delay neural networks via augmented Lyapunov-Krasovskii functionals, Appl. Math. Comput., 338 (2018), 869-881.  doi: 10.1016/j.amc.2018.05.059.

[10]

L. O. Chua and L. Yang, Cellular neural networks: Applications, IEEE Trans. Circuits and Systems: Part-I, 35 (1988), 1273-1290.  doi: 10.1109/31.7601.

[11]

M. A. Cohen and S. Grossberg, Absolute stability of global pattern formation and parallel memory storage by competitive neural networks, IEEE Trans. Systems Man Cybernet., 13 (1983), 815-826. 

[12]

Z. DongX. Zhang and X. Wang, Global exponential stability of discrete-time higher-order Cohen-Grossberg neural networks with time-varying delays, connection weights and impulses, J. Franklin Inst., 358 (2021), 5931-5950.  doi: 10.1016/j.jfranklin.2021.05.020.

[13]

O. Faydasicok and S. Arik, Equilibrium and stability analysis of delayed neural networks under parameter uncertainties, Appl. Math. Comput., 218 (2012), 6716-6726.  doi: 10.1016/j.amc.2011.12.036.

[14]

O. Faydasicok and S. Arik, An analysis of stability of uncertain neural networks with multiple time delays, J. Franklin Inst., 350 (2013), 1808-1826.  doi: 10.1016/j.jfranklin.2013.05.006.

[15]

J. J. Hopfield, Neural networks and physical systems with emergent collective computational abilities, Proc. Nat. Acad. Sci. U.S.A., 79 (1982), 2554-2558.  doi: 10.1073/pnas.79.8.2554.

[16]

X. Li and P. Li, Stability of time-delay systems with impulsive control involving stabilizing delays, Automatica J. IFAC, 124 (2021), 109336, 6 pp. doi: 10.1016/j.automatica.2020.109336.

[17]

X. LiD. Peng and J. Cao, Lyapunov stability for impulsive systems via event-triggered impulsive control, IEEE Trans. Automat. Control, 65 (2020), 4908-4913.  doi: 10.1109/TAC.2020.2964558.

[18]

X. LiS. Song and J. Wu, Exponential stability of nonlinear systems with delayed impulses and applications, IEEE Trans. Automat. Control, 64 (2019), 4024-4034.  doi: 10.1109/TAC.2019.2905271.

[19]

X. LiX. Yang and S. Song, Lyapunov conditions for finite-time stability of time-varying time-delay systems, Automatica J. IFAC, 103 (2019), 135-140.  doi: 10.1016/j.automatica.2019.01.031.

[20]

X. LiaoK.-W. WongZ. Wu and G. Chen, Novel robust stability for interval-delayed hopfield neural, IEEE Trans. Circuits Systems I Fund. Theory Appl., 48 (2001), 1355-1359.  doi: 10.1109/81.964428.

[21]

N. Ozcan and S. Arik, New global robust stability condition for uncertain neural networks with time delays, Neurocomputing, 142 (2014), 267-274.  doi: 10.1016/j.neucom.2014.04.040.

[22]

J. Pan and Z. Pan, Novel robust stability criteria for uncertain parameter quaternionic neural networks with mixed delays: Whole quaternionic method, Appl. Math. Comput., 407 (2021), 126326, 15 pp. doi: 10.1016/j.amc.2021.126326.

[23]

L. Rong and T. Chen, New results on the robust stability of Cohen-Grossberg neural networks with delays, Neural Processing Letters, 24 (2006), 193-202. 

[24]

R. Samli, A new delay-independent condition for global robust stability of neural networks with time delays, Neural Networks, 66 (2015), 131-137.  doi: 10.1016/j.neunet.2015.03.004.

[25]

S. Senan, Robustness analysis of uncertain dynamical neural networks with multiple time delays, Neural Networks, 70 (2015), 53-60.  doi: 10.1016/j.neunet.2015.07.001.

[26]

Q. SongQ. YuZ. ZhaoY. Liu and F. E. Alsaadi, Boundedness and global robust stability analysis of delayed complex-valued neural networks with interval parameter uncertainties, Neural Networks, 103 (2018), 55-62. 

[27]

Q. Xiao and T. Huang, Stability of delayed inertial neural networks on time scales: A unified matrix-measure approach, Neural Networks, 130 (2020), 33-38.  doi: 10.1016/j.neunet.2020.06.020.

[28]

H. XueX. XuJ. Zhang and X. Yang, Robust stability of impulsive switched neural networks with multiple time delays, Appl. Math. Comput., 359 (2019), 456-475.  doi: 10.1016/j.amc.2019.04.063.

[29]

C.-K. ZhangY. HeL. JiangW.-J. Lin and 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.  doi: 10.1016/j.amc.2016.08.043.

show all references

References:
[1]

S. Arik, New criteria for global robust stability of delayed neural networks with norm-bounded uncertainties, IEEE Transactions on Neural Networks and Learning Systems, 25 (2014), 1045-1052. 

[2]

S. Arik, Further analysis of stability of uncertain neural networks with multiple time delays, Adv. Difference Equ., 2014 (2014), 41, 16 pp. doi: 10.1186/1687-1847-2014-41.

[3]

S. Arik, Dynamical analysis of uncertain neural networks with multiple time delays, Internat. J. Systems Sci., 47 (2016), 730-739.  doi: 10.1080/00207721.2014.902158.

[4]

E. Arslan, Novel criteria for global robust stability of dynamical neural networks with multiple time delays, Neural Networks, 142 (2021), 119-127.  doi: 10.1016/j.neunet.2021.04.039.

[5]

Y. CaoR. SriramanN. Shyamsundarraj and R. Samidurai, Robust stability of uncertain stochastic complex-valued neural networks with additive time-varying delays, Math. Comput. Simulation, 171 (2020), 207-220.  doi: 10.1016/j.matcom.2019.05.011.

[6]

J. ChenB. Chen and Z. Zeng, Basic theorem and global exponential stability of differential algebraic neural networks with delay, Neural Networks, 140 (2021), 336-343.  doi: 10.1016/j.neunet.2021.01.017.

[7]

S. ChenQ. SongZ. ZhaoY. Liu and F. E. Alsaadi, Global asymptotic stability of fractional-order complex-valued neural networks with probabilistic time-varying delays, Neurocomputing, 450 (2021), 311-318.  doi: 10.1016/j.neucom.2021.04.043.

[8]

T. Chen and L. Rong, Robust global exponential stability of Cohen-Grossberg neural networks with time delays, IEEE Transactions on Neural Networks, 15 (2004), 203-206. 

[9]

Y. ChenZ. WangY. Liu and F. E. Alsaadi, Stochastic stability for distributed delay neural networks via augmented Lyapunov-Krasovskii functionals, Appl. Math. Comput., 338 (2018), 869-881.  doi: 10.1016/j.amc.2018.05.059.

[10]

L. O. Chua and L. Yang, Cellular neural networks: Applications, IEEE Trans. Circuits and Systems: Part-I, 35 (1988), 1273-1290.  doi: 10.1109/31.7601.

[11]

M. A. Cohen and S. Grossberg, Absolute stability of global pattern formation and parallel memory storage by competitive neural networks, IEEE Trans. Systems Man Cybernet., 13 (1983), 815-826. 

[12]

Z. DongX. Zhang and X. Wang, Global exponential stability of discrete-time higher-order Cohen-Grossberg neural networks with time-varying delays, connection weights and impulses, J. Franklin Inst., 358 (2021), 5931-5950.  doi: 10.1016/j.jfranklin.2021.05.020.

[13]

O. Faydasicok and S. Arik, Equilibrium and stability analysis of delayed neural networks under parameter uncertainties, Appl. Math. Comput., 218 (2012), 6716-6726.  doi: 10.1016/j.amc.2011.12.036.

[14]

O. Faydasicok and S. Arik, An analysis of stability of uncertain neural networks with multiple time delays, J. Franklin Inst., 350 (2013), 1808-1826.  doi: 10.1016/j.jfranklin.2013.05.006.

[15]

J. J. Hopfield, Neural networks and physical systems with emergent collective computational abilities, Proc. Nat. Acad. Sci. U.S.A., 79 (1982), 2554-2558.  doi: 10.1073/pnas.79.8.2554.

[16]

X. Li and P. Li, Stability of time-delay systems with impulsive control involving stabilizing delays, Automatica J. IFAC, 124 (2021), 109336, 6 pp. doi: 10.1016/j.automatica.2020.109336.

[17]

X. LiD. Peng and J. Cao, Lyapunov stability for impulsive systems via event-triggered impulsive control, IEEE Trans. Automat. Control, 65 (2020), 4908-4913.  doi: 10.1109/TAC.2020.2964558.

[18]

X. LiS. Song and J. Wu, Exponential stability of nonlinear systems with delayed impulses and applications, IEEE Trans. Automat. Control, 64 (2019), 4024-4034.  doi: 10.1109/TAC.2019.2905271.

[19]

X. LiX. Yang and S. Song, Lyapunov conditions for finite-time stability of time-varying time-delay systems, Automatica J. IFAC, 103 (2019), 135-140.  doi: 10.1016/j.automatica.2019.01.031.

[20]

X. LiaoK.-W. WongZ. Wu and G. Chen, Novel robust stability for interval-delayed hopfield neural, IEEE Trans. Circuits Systems I Fund. Theory Appl., 48 (2001), 1355-1359.  doi: 10.1109/81.964428.

[21]

N. Ozcan and S. Arik, New global robust stability condition for uncertain neural networks with time delays, Neurocomputing, 142 (2014), 267-274.  doi: 10.1016/j.neucom.2014.04.040.

[22]

J. Pan and Z. Pan, Novel robust stability criteria for uncertain parameter quaternionic neural networks with mixed delays: Whole quaternionic method, Appl. Math. Comput., 407 (2021), 126326, 15 pp. doi: 10.1016/j.amc.2021.126326.

[23]

L. Rong and T. Chen, New results on the robust stability of Cohen-Grossberg neural networks with delays, Neural Processing Letters, 24 (2006), 193-202. 

[24]

R. Samli, A new delay-independent condition for global robust stability of neural networks with time delays, Neural Networks, 66 (2015), 131-137.  doi: 10.1016/j.neunet.2015.03.004.

[25]

S. Senan, Robustness analysis of uncertain dynamical neural networks with multiple time delays, Neural Networks, 70 (2015), 53-60.  doi: 10.1016/j.neunet.2015.07.001.

[26]

Q. SongQ. YuZ. ZhaoY. Liu and F. E. Alsaadi, Boundedness and global robust stability analysis of delayed complex-valued neural networks with interval parameter uncertainties, Neural Networks, 103 (2018), 55-62. 

[27]

Q. Xiao and T. Huang, Stability of delayed inertial neural networks on time scales: A unified matrix-measure approach, Neural Networks, 130 (2020), 33-38.  doi: 10.1016/j.neunet.2020.06.020.

[28]

H. XueX. XuJ. Zhang and X. Yang, Robust stability of impulsive switched neural networks with multiple time delays, Appl. Math. Comput., 359 (2019), 456-475.  doi: 10.1016/j.amc.2019.04.063.

[29]

C.-K. ZhangY. HeL. JiangW.-J. Lin and 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.  doi: 10.1016/j.amc.2016.08.043.

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