Improved results on an extended dissipative analysis of neural networks with additive time-varying delays using auxiliary function-based integral inequalities

Saravanan Shanmugam; R. Vadivel; Mohamed Rhaima; Hamza Ghoudi; Saravanan Shanmugam; R. Vadivel; Mohamed Rhaima; Hamza Ghoudi

doi:10.3934/math.20231082

AIMS Mathematics

2023, Volume 8, Issue 9: 21221-21245. doi: 10.3934/math.20231082

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Research article

Improved results on an extended dissipative analysis of neural networks with additive time-varying delays using auxiliary function-based integral inequalities

1.
Centre for Nonlinear Systems, Chennai Institute of Technology, Chennai 600069, Tamilnadu, India
2.
Department of Mathematics, Faculty of Science and Technology, Phuket Rajabhat University, Phuket 83000, Thailand
3.
Department of Statistics and Operations Research, College of Sciences, King Saud University, Riyadh 11451, Saudi Arabia
4.
University of Paris Nanterre, MODAL'X, BAT G, 200, ave de la République 92000 Nanterre, France

Received: 05 May 2023 Revised: 07 June 2023 Accepted: 20 June 2023 Published: 03 July 2023
MSC : 93D20, 92B20

The issue of extended dissipative analysis for neural networks (NNs) with additive time-varying delays (ATVDs) is examined in this research. Some less conservative sufficient conditions are obtained to ensure the NNs are asymptotically stable and extended dissipative by building the agumented Lyapunov-Krasovskii functional, which is achieved by utilizing some mathematical techniques with improved integral inequalities like auxiliary function-based integral inequalities (gives a tighter upper bound). The present study aims to solve the $ H_{\infty}, L_2-L_{\infty} $, passivity and $ (Q, S, R) $-$ \gamma $-dissipativity performance in a unified framework based on the extended dissipativity concept. Following this, the condition for the solvability of the designed NNs with ATVDs is presented in the form of linear matrix inequalities. Finally, the practicality and effectiveness of this approach were demonstrated through four numerical examples.
- neural networks,
- linear matrix inequality,
- extended dissipative,
- additive time-varying delay,
- Lyapunov-Krasovskii functional
Citation: Saravanan Shanmugam, R. Vadivel, Mohamed Rhaima, Hamza Ghoudi. Improved results on an extended dissipative analysis of neural networks with additive time-varying delays using auxiliary function-based integral inequalities[J]. AIMS Mathematics, 2023, 8(9): 21221-21245. doi: 10.3934/math.20231082

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Abstract

The issue of extended dissipative analysis for neural networks (NNs) with additive time-varying delays (ATVDs) is examined in this research. Some less conservative sufficient conditions are obtained to ensure the NNs are asymptotically stable and extended dissipative by building the agumented Lyapunov-Krasovskii functional, which is achieved by utilizing some mathematical techniques with improved integral inequalities like auxiliary function-based integral inequalities (gives a tighter upper bound). The present study aims to solve the $ H_{\infty}, L_2-L_{\infty} $, passivity and $ (Q, S, R) $-$ \gamma $-dissipativity performance in a unified framework based on the extended dissipativity concept. Following this, the condition for the solvability of the designed NNs with ATVDs is presented in the form of linear matrix inequalities. Finally, the practicality and effectiveness of this approach were demonstrated through four numerical examples.

References

[1]	Y. He, M. Wu, J. H. She, Delay-dependent exponential stability of delayed neural networks with time-varying delay, IEEE T. Circuits-II, 53 (2006), 553–557. https://doi.org/10.1109/TCSII.2006.876385 doi: 10.1109/TCSII.2006.876385
[2]	Q. Jia, E. S. Mwanandiye, W. K. Tang, Master-slave synchronization of delayed neural networks with time-varying control, IEEE T. Neur. Net. Lear., 32 (2020), 2292–2298. https://doi.org/10.1109/TNNLS.2020.2996224 doi: 10.1109/TNNLS.2020.2996224
[3]	Z. Cai, L. Huang, L. Zhang, New exponential synchronization criteria for time-varying delayed neural networks with discontinuous activations, Neural Networks, 65 (2015), 105–114. https://doi.org/10.1016/j.neunet.2015.02.001 doi: 10.1016/j.neunet.2015.02.001
[4]	L. Sun, Y. Tang, W. Wang, S. Shen, Stability analysis of time-varying delay neural networks based on new integral inequalities, J. Franklin I., 357 (2020), 10828–10843. https://doi.org/10.1016/j.jfranklin.2020.08.017 doi: 10.1016/j.jfranklin.2020.08.017
[5]	H. Huang, G. Feng, J. Cao, Robust state estimation for uncertain neural networks with time-varying delay, IEEE T. Neural Network., 19 (2008), 1329–1339. https://doi.org/10.1109/TNN.2008.2000206 doi: 10.1109/TNN.2008.2000206
[6]	J. Nong, Global exponential stability of delayed hopfield neural networks, In: 2012 International Conference on Computer Science and Information Processing (CSIP), 2012.
[7]	C. R. Wang, Y. He, W. J. Lin, Stability analysis of generalized neural networks with fast-varying delay via a relaxed negative-determination quadratic function method, Appl. Math. Comput., 391 (2021), 125631. https://doi.org/10.1016/j.amc.2020.125631 doi: 10.1016/j.amc.2020.125631
[8]	M. S. Ali, S. Arik, R. Saravanakumar, Delay-dependent stability criteria of uncertain {M}arkovian jump neural networks with discrete interval and distributed time-varying delays, Neurocomputing, 158 (2015), 167–173. https://doi.org/10.1016/j.neucom.2015.01.056 doi: 10.1016/j.neucom.2015.01.056
[9]	S. Saravanan, M. S. Ali, Improved results on finite-time stability analysis of neural networks with time-varying delays, J. Dyn. Syst., 140 (2018), 101003. https://doi.org/10.1115/1.4039667 doi: 10.1115/1.4039667
[10]	E. M. Asl, F. Hashemzadeh, M. Baradarannia, P. Bagheri, The effect of observer position on networked control systems with random transmission delays and packet dropouts, In: 2022 8th International Conference on Control, Instrumentation and Automation (ICCIA), 2022. https://doi.org/10.1109/ICCIA54998.2022.9737196
[11]	J. Lam, H. Gao, C. Wang, Stability analysis for continuous systems with two additive time-varying delay components, Syst. Control Lett., 56 (2007), 16–24. https://doi.org/10.1016/j.sysconle.2006.07.005 doi: 10.1016/j.sysconle.2006.07.005
[12]	N. Xiao, Y. Jia, New approaches on stability criteria for neural networks with two additive time-varying delay components, Neurocomputing, 118 (2013), 150–156. https://doi.org/10.1016/j.neucom.2013.02.028 doi: 10.1016/j.neucom.2013.02.028
[13]	J. Cheng, H. Zhu, S. Zhong, Y. Zhang, Y. Zeng, Improved delay-dependent stability criteria for continuous system with two additive time-varying delay components, Commun. Nonlinear Sci., 19 (2014), 210–215. https://doi.org/10.1016/j.cnsns.2013.05.026 doi: 10.1016/j.cnsns.2013.05.026
[14]	J. Tian, S. Zhong, Improved delay-dependent stability criteria for neural networks with two additive time-varying delay components, Neurocomputing, 77 (2012), 114–119. https://doi.org/10.1016/j.neucom.2011.08.027 doi: 10.1016/j.neucom.2011.08.027
[15]	C. K. Zhang, Y. He, L. Jiang, Q. Wu, M. Wu, Delay-dependent stability criteria for generalized neural networks with two delay components, IEEE T. Neur. Net. Lear., 25 (2013), 1263–1276. https://doi.org/10.1109/TNNLS.2013.2284968 doi: 10.1109/TNNLS.2013.2284968
[16]	Y. Liu, S. M. Lee, H. Lee, Robust delay-depent stability criteria for uncertain neural networks with two additive time-varying delay components, Neurocomputing, 151 (2015), 770–775. https://doi.org/10.1016/j.neucom.2014.10.023 doi: 10.1016/j.neucom.2014.10.023
[17]	L. Ding, Y. He, Y. Liao, M. Wu, New result for generalized neural networks with additive time-varying delays using free-matrix-based integral inequality method, Neurocomputing, 238 (2017), 205–211. https://doi.org/10.1016/j.neucom.2017.01.056 doi: 10.1016/j.neucom.2017.01.056
[18]	R. Rakkiyappan, A. Chandrasekar, J. Cao, Passivity and passification of memristor-based recurrent neural networks with additive time-varying delays, IEEE T. Neur. Net. Lear., 26 (2014), 2043–2057. https://doi.org/10.1109/TNNLS.2014.2365059 doi: 10.1109/TNNLS.2014.2365059
[19]	K. Subramanian, P. Muthukumar, Global asymptotic stability of complex-valued neural networks with additive time-varying delays, Cogn. Neurodynamics, 11 (2017), 293–306. https://doi.org/10.1007/s11571-017-9429-1 doi: 10.1007/s11571-017-9429-1
[20]	L. Xiong, Y. Li, W. Zhou, Improved stabilization for continuous dynamical systems with two additive time-varying delays, Asian J. Control, 17 (2015), 2229–2240. https://doi.org/10.1002/asjc.1124 doi: 10.1002/asjc.1124
[21]	M. S. Ali, S. Saravanan, J. Cao, Finite-time boundedness, ${L}_2$-gain analysis and control of {M}arkovian jump switched neural networks with additive time-varying delays, Nonlinear Anal. Hybri., 23 (2017), 27–43. https://doi.org/10.1016/j.nahs.2016.06.004 doi: 10.1016/j.nahs.2016.06.004
[22]	R. Li, J. Cao, Passivity and dissipativity of fractional-order quaternion-valued fuzzy memristive neural networks: Nonlinear scalarization approach, IEEE T. Cybernetics, 52 (2020), 2821–2832. https://doi.org/10.1109/TCYB.2020.3025439 doi: 10.1109/TCYB.2020.3025439
[23]	Z. G. Wu, J. Lam, H. Su, J. Chu, Stability and dissipativity analysis of static neural networks with time delay, IEEE T. Neur. Net. Lear., 23 (2011), 199–210. https://doi.org/10.1109/TNNLS.2011.2178563 doi: 10.1109/TNNLS.2011.2178563
[24]	H. Sang, H. Nie, J. Zhao, Dissipativity-based synchronization for switched discrete-time-delayed neural networks with combined switching paradigm, IEEE T. Cybernetics, 52 (2021), 7995–8005. https://doi.org/10.1109/TCYB.2021.3052160 doi: 10.1109/TCYB.2021.3052160
[25]	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. Franklin I., 352 (2015), 1284–1295. http://doi.org/10.1016/j.jfranklin.2014.12.023 doi: 10.1016/j.jfranklin.2014.12.023
[26]	K. Mathiyalagan, J. H. Park, R. Sakthivel, Observer-based dissipative control for networked control systems: A switched system approach, Complexity, 21 (2015), 297–308. https://doi.org/10.1002/cplx.21605 doi: 10.1002/cplx.21605
[27]	B. Zhang, W. X. Zheng, S. Xu, Filtering of {M}arkovian jump delay systems based on a new performance index, IEEE T. Circuits-I, 60 (2013), 1250–1263. https://doi.org/10.1109/TCSI.2013.2246213 doi: 10.1109/TCSI.2013.2246213
[28]	T. H. Lee, M. J. Park, J. H. Park, O. M. Kwon, S. M. Lee, Extended dissipative analysis for neural networks with time-varying delays, IEEE T. Neur. Net. Lear., 25 (2014), 1936–1941. https://doi.org/10.1109/TNNLS.2013.2296514 doi: 10.1109/TNNLS.2013.2296514
[29]	R. Saravanakumar, G. Rajchakit, M. S. Ali, Y. H. Joo, Extended dissipativity of generalised neural networks including time delays, Int. J. Syst. Sci., 48 (2017), 2311–2320. https://doi.org/10.1080/00207721.2017.1316882 doi: 10.1080/00207721.2017.1316882
[30]	R. Saravanakumar, H. Mukaidani, P. Muthukumar, Extended dissipative state estimation of delayed stochastic neural networks, Neurocomputing, 406 (2020), 244–252. https://doi.org/10.1016/j.neucom.2020.03.106 doi: 10.1016/j.neucom.2020.03.106
[31]	S. Shanmugam, S. A. Muhammed, G. M. Lee, Finite-time extended dissipativity of delayed {T}akagi-{S}ugeno fuzzy neural networks using a free-matrix-based double integral inequality, Neural Comput. Appl., 32 (2020), 8517–8528. https://doi.org/10.1007/s00521-019-04348-w doi: 10.1007/s00521-019-04348-w
[32]	R. Vadivel, P. Hammachukiattikul, S. Vinoth, K. Chaisena, N. Gunasekaran, An extended dissipative analysis of fractional-order fuzzy networked control systems, Fractal Fract., 6 (2022), 591. https://doi.org/10.3390/fractalfract6100591 doi: 10.3390/fractalfract6100591
[33]	R. Anbuvithya, S. D. Sri, R. Vadivel, P. Hammachukiattikul, C. Park, G. Nallappan, Extended dissipativity synchronization for {M}arkovian jump recurrent neural networks via memory sampled-data control and its application to circuit theory, Int. J. Nonlinear Anal., 13 (2022), 2801–2820.
[34]	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. https://doi.org/10.1016/j.neucom.2015.07.004 doi: 10.1016/j.neucom.2015.07.004
[35]	P. Muthukumar, K. Subramanian, Stability criteria for markovian jump neural networks with mode-dependent additive time-varying delays via quadratic convex combination, Neurocomputing, 205 (2016), 75–83. https://doi.org/10.1016/j.neucom.2016.03.058 doi: 10.1016/j.neucom.2016.03.058
[36]	F. Liu, H. Liu, K. Liu, New asymptotic stability analysis for generalized neural networks with additive time-varying delays and general activation function, Neurocomputing, 463 (2021), 437–443. https://doi.org/10.1016/j.neucom.2021.08.066 doi: 10.1016/j.neucom.2021.08.066
[37]	P. Park, W. I. Lee, S. Y. Lee, Auxiliary function-based integral inequalities for quadratic functions and their applications to time-delay systems, J. Franklin I., 352 (2015), 1378–1396. https://doi.org/10.1016/j.jfranklin.2015.01.004 doi: 10.1016/j.jfranklin.2015.01.004
[38]	P. 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
[39]	J. Cheng, L. Xiong, Improved integral inequality approach on stabilization for continuous-time systems with time-varying input delay, Neurocomputing, 160 (2015), 274–280. https://doi.org/10.1016/j.neucom.2015.02.026 doi: 10.1016/j.neucom.2015.02.026
[40]	H. Shao, Q. L. Han, New delay-dependent stability criteria for neural networks with two additive time-varying delay components, IEEE T. Neural Network., 22 (2011), 812–818. https://doi.org/10.1109/TNN.2011.2114366 doi: 10.1109/TNN.2011.2114366
[41]	K. H. Johansson, The quadruple-tank process: A multivariable laboratory process with an adjustable zero, IEEE T. Contr. Syst. T., 8 (2000), 456–465. https://doi.org/10.1109/87.845876 doi: 10.1109/87.845876
[42]	T. Huang, C. Li, S. Duan, J. A. Starzyk, Robust exponential stability of uncertain delayed neural networks with stochastic perturbation and impulse effects, IEEE T. Neur. Net. Lear., 23 (2012), 866–875. https://doi.org/10.1109/TNNLS.2012.2192135 doi: 10.1109/TNNLS.2012.2192135
[43]	T. H. Lee, J. H. Park, O. Kwon, S. M. Lee, Stochastic sampled-data control for state estimation of time-varying delayed neural networks, Neural Networks, 46 (2013), 99–108. https://doi.org/10.1016/j.neunet.2013.05.001 doi: 10.1016/j.neunet.2013.05.001
[44]	M. S. Ali, N. Gunasekaran, R. Saravanakumar, Design of passivity and passification for delayed neural networks with markovian jump parameters via non-uniform sampled-data control, Neural Comput. Appl., 30 (2018), 595–605. https://doi.org/10.1007/s00521-016-2682-0 doi: 10.1007/s00521-016-2682-0

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