Improvement of finite-time stability for delayed neural networks via a new Lyapunov-Krasovskii functional

Patarawadee Prasertsang; Thongchai Botmart; Patarawadee Prasertsang; Thongchai Botmart

doi:10.3934/math.2021060

AIMS Mathematics

2021, Volume 6, Issue 1: 998-1023. doi: 10.3934/math.2021060

Previous Article Next Article

Research article Special Issues

Improvement of finite-time stability for delayed neural networks via a new Lyapunov-Krasovskii functional

Patarawadee Prasertsang ¹,
Thongchai Botmart ^{2
,
,}

1.
Department of General Science, Kasetsart University, Chalermprakiat Sakon Nakhon Province Campus, Sakon Nakhon 47000, Thailand
2.
Department of Mathematics, Faculty of Science, Khon Kaen University, Khon Kaen 40002, Thailand

Received: 04 September 2020 Accepted: 03 November 2020 Published: 06 November 2020
MSC : 34D20, 34K20, 37C75

The topic of finite-time stability criterion for neural networks with time-varying delays via a new argument Lyapunov-Krasovskii functional (LKF) was proposed and the time-varying delay of the system is without differentiable. For sufficient conditions of this study, a new (LKF) is combined with improved triple integral terms, namely the functionality of finite-time stability, integral inequality, and a positive diagonal matrix without using a free weighting matrix. The improved finite-time sufficient conditions for the neural network with time varying delay are given in terms of linear matrix inequalities (LMIs) and the results show improvement on previous studies. Numerical examples are given to illustrate the effectiveness of the proposed method.
- finite-time stability,
- neural networks,
- time-varying delays,
- integral inequality
Citation: Patarawadee Prasertsang, Thongchai Botmart. Improvement of finite-time stability for delayed neural networks via a new Lyapunov-Krasovskii functional[J]. AIMS Mathematics, 2021, 6(1): 998-1023. doi: 10.3934/math.2021060

Related Papers:

Abstract

The topic of finite-time stability criterion for neural networks with time-varying delays via a new argument Lyapunov-Krasovskii functional (LKF) was proposed and the time-varying delay of the system is without differentiable. For sufficient conditions of this study, a new (LKF) is combined with improved triple integral terms, namely the functionality of finite-time stability, integral inequality, and a positive diagonal matrix without using a free weighting matrix. The improved finite-time sufficient conditions for the neural network with time varying delay are given in terms of linear matrix inequalities (LMIs) and the results show improvement on previous studies. Numerical examples are given to illustrate the effectiveness of the proposed method.

References

[1]	Y. Q. Bai, J. Chen, New stability criteria for recurrent neural networks with interval time-varying delay, Neurocomputing, 121 (2013), 179-184. doi: 10.1016/j.neucom.2013.04.031
[2]	J. Sun, J. Chen, Stability analysis of static recurrent neural networks with interval time-varying delay, Appl Math Comput, 221 (2013), 111-120.
[3]	O. M. Kwon, M. J. Park, J. H. Park, S. M. Lee, E. J. Cha, New and improved results on stability of static neural networks with interval time-varying delays, Appl Math Comput, 239 (2014), 346-357.
[4]	H. B. Zeng, J. H. Park, C. F. Zhang, W. Wang, Stability and dissipativity analysis of static neural networks with interval time-varying delay, J. Frankl. Inst., 352 (2015), 1284-1295. doi: 10.1016/j.jfranklin.2014.12.023
[5]	W. J. Lin, Y. He, C. K. Zhang, M. Wu, M. Ji, Stability analysis of recurrent neural networks with interval time-varying delay via free-matrix-based integral inequality, Neurocomputing, 205 (2016), 490-497. doi: 10.1016/j.neucom.2016.04.052
[6]	Z. M. Gao, Y. He, M. Wu, Improved stability criteria for the neural networks with time-varying delay via new augmented Lyapunov-Krasovskii functional, Appl. Math. Comput., 349 (2019), 258-269.
[7]	X. M. Zhang, Q. L. Han, Global asymptotic stability analysis for delayed neural networks using a matrix-based quadratic convex approach, Neural Networks, 54 (2014), 57-69. doi: 10.1016/j.neunet.2014.02.012
[8]	O. M. Kwon, J. H. Park, S. M. Lee, E. J. Cha, Analysis on delay-dependent stability for neural networks with time-varying delays, Neurocomputing, 103 (2013), 114-120. doi: 10.1016/j.neucom.2012.09.012
[9]	X. Xie, Z. Ren, Improved delay-dependent stability analysis for neural networks with time-varying delays, ISA Trans., 53 (2014), 1000-1005. doi: 10.1016/j.isatra.2014.05.010
[10]	M. D. Ji, Y. He, C. K. Zhang, M. Mu, Novel stability criteria for recurrent neural networks with time-varying delay, Neurocomputing, 138 (2014), 383-391. doi: 10.1016/j.neucom.2014.01.024
[11]	O. M. Kwon, M. J. Park, J. H. Park, S. M. Lee, E. J. Cha, On stability analysis for neural networks with interval time-varying delays via some new augmented Lyapunov-Krasovskii functional, Commun. Nonlinear Sci. Numer. Simulat., 19 (2014), 3184-3201. doi: 10.1016/j.cnsns.2014.02.024
[12]	W. I. Lee, S. Y. Lee, P. G. Park, Improved stability criteria for recurrent neural networks with interval time-varying delays via new Lyapunov functionals, Neurocomputing, 155 (2015), 128-134. doi: 10.1016/j.neucom.2014.12.040
[13]	X. Wang, K. She, S. Zhong, S. Yang, New and improved results for recurrent neural networks with interval time-varying delay, Neurocomputing, 175A (2016), 492-499.
[14]	Y. Zhang, D. Yue, E. Tian, New stability criteria of neural networks with interval time-varying delay: A piecewise delay method, Appl. Math. Comput., 208 (2009), 249-259.
[15]	Q. Yang, Q. Ren, X. Xie, New delay dependent stability criteria for recurrent neural networks with interval time-varying delay, ISA Trans., 53 (2014), 994-999. doi: 10.1016/j.isatra.2014.05.009
[16]	R. Rakkiyappan, R. Sivasamy, J. H. Park, T. H. Lee, An improved stability criterion for generalized neural networks with additive time-varying delays, Neurocomputing, 171 (2016), 615-624. doi: 10.1016/j.neucom.2015.07.004
[17]	H. B. Zeng, Y. He, P. Shi, M. Wu, S. P. Xiao, Dissipativity analysis of neural networks with time-varying delays, Neurocomputing, 168 (2015), 741-746. doi: 10.1016/j.neucom.2015.05.050
[18]	H. T. Wang, Z. T. Liu, Y. He, Exponential stability criterion of the switched neural networks with time-varying delay, Neurocomputing, 331 (2019), 1-9. doi: 10.1016/j.neucom.2018.11.022
[19]	J. Tian, S. Zhong, Improved delay-dependent stability criterion for neural networks with time-varying delay, Appl. Math. Comput., 217 (2011), 10278-10288.
[20]	S. Senthilraj, R. Raja, Q. Zhu, R. Samidurai, Z. Yao, New delay-interval-dependent stability criteria for static neural networks with time-varying delays, Neurocomputing, 186 (2016), 1-7. doi: 10.1016/j.neucom.2015.12.063
[21]	M. J. Park, O. M. Kwon, J. H. Park, S. M. Lee, E. J. Cha, On synchronization criterion for coupled discrete-time neural networks with interval time-varying delays, Neurocomputing, 99 (2013), 188-196. doi: 10.1016/j.neucom.2012.04.027
[22]	B. Yang, J. Wang, X. Liu, Improved delay-dependent stability criteria for generalized neural networks with time-varying delays, Inf. Sci., 420 (2017), 299-312. doi: 10.1016/j.ins.2017.08.072
[23]	M. J. Park, S. H. Lee, O. M. Kwon, J. H. Ryu, Enhanced stability criteria of neural networks with time-varying delays via a generalized free-weighting matrix integral inequality, J. Frankl. Inst., 355 (2018), 6531-6548. doi: 10.1016/j.jfranklin.2018.06.023
[24]	C. Hua, Y. Wang, S. Wu, Stability analysis of neural networks with time-varying delay using a new augmented Lyapunov-Krasovskii functional, Neurocomputing, 332 (2019), 1-9. doi: 10.1016/j.neucom.2018.08.044
[25]	F. Zhang, Z. Li, Auxiliary function-based integral inequality approach to robust passivity analysis of neural networks with interval time-varying delay, Neurocomputing, 306 (2018), 189-199. doi: 10.1016/j.neucom.2018.04.026
[26]	X. Yang, Y. Tian, X. Li, Finite-time boundedness and stabilization of uncertain switched delayed neural networks of neutral type, Neurocomputing, 314 (2018), 468-478. doi: 10.1016/j.neucom.2018.07.020
[27]	J. Xiao, Z. Zeng, A. Wu, New criteria for exponential stability of delayed recurrent neural networks, Neurocomputing, 134 (2014), 182-188. doi: 10.1016/j.neucom.2013.07.053
[28]	B. Yang, J. Wang, J. Wang, Stability analysis of delayed neural networks via a new integral inequality, Neural Networks, 88 (2017), 49-57. doi: 10.1016/j.neunet.2017.01.008
[29]	X. Yang, Q. Song, Y. Liu, Z. Zhao, Finite-time stability analysis of fractional-order neural networks with delay, Neurocomputing, 152 (2015), 19-26. doi: 10.1016/j.neucom.2014.11.023
[30]	M. S. Ali, S. Saravanan, Finite-time stability for memristor base d switched neural networks with time-varying delays via average dwell time approach, Neurocomputing, 275 (2018), 1637-1649. doi: 10.1016/j.neucom.2017.10.003
[31]	A. Pratap, R. Raja, J. Cao, J. Alzabut, C. Huang, Finite-time synchronization criterion of graph theory perspective fractional-order coupled discontinuous neural networks, Adv. Differ. Equ., 97 (2020), 1-24.
[32]	A. Pratap, R. Raja, J. Cao, G. Rajchakit, F. E. Alsaadi, Further synchronization in finite time analysis for time-varying delayed fractional order memristive competitive neural networks with leakage delay, Neurocomputing, 317 (2018), 110-126. doi: 10.1016/j.neucom.2018.08.016
[33]	A. Pratap, R. Raja, J. Alzabut, J. Dianavinnarasi, J. Cao, G. Rajchakit, Finite-time Mittag-Leffler stability of fractional-order quaternion-valued memristive neural networks with impulses, Neural Process. Lett., 512 (2020), 1485-1526.
[34]	J. Puangmalai, J. Tongkum, T. Rojsiraphisal, Finite-time stability criteria of linear system with non-differentiable time-varying delay via new integral inequality, Math. Comput. Simulat., 171 (2020), 170-186. doi: 10.1016/j.matcom.2019.06.013
[35]	J. Li, H. Jiang, C. Hu, J. Yu, Analysis and discontinuous control for finite-time synchronization of delayed complex dynamical networks, Chaos, Solitons Fractals, 114 (2018), 291-305. doi: 10.1016/j.chaos.2018.07.019
[36]	X. Liu, X. Liu, M. Tang, F. Wang, Improved exponential stability criterion for neural networks with time-varying delay, Neurocomputing, 234 (2017), 154-163. doi: 10.1016/j.neucom.2016.12.057
[37]	M. Zheng, L. Li, H. Peng, J. Xiao, Y. Yang, H. Zhao, Finite-time stability analysis for neutral-type neural networks with hybrid time-varying delays without using Lyapunov method, Neurocomputing, 238 (2017), 67-75. doi: 10.1016/j.neucom.2017.01.037
[38]	M. Zheng, L. Li, H. Peng, J. Xiao, Y. Yang, Y. Zhang, H. Zhao, Finite-time stability and synchronization of memristor-based fractional-order fuzzy cellular neural networks, Commun. Nonlinear Sci. Numer. Simulat., 59 (2018), 272-297. doi: 10.1016/j.cnsns.2017.11.025
[39]	B. Wu, C. Wang, A generalized multiple-integral inequality and its application on stability analysis for time-varying delay systems, J. Frankl. Inst., 356 (2019), 4026-4042. doi: 10.1016/j.jfranklin.2019.02.003
[40]	S. Boyd, E. L. Ghaoui, E. Feron, V. Balakrishnan, Linear Matrix Inequalities in System and Control Theory, SIAM, Philadephia, 1994.
[41]	J. Sun, G. P. Liu, J. Chen, Delay-dependent stability and stabilization of neutral time-delay systems, Int. J. Robust Nonlinear Control, 19 (2009), 1364-1375. doi: 10.1002/rnc.1384

Reader Comments

Your name:*

Email:*
© 2021 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)