×

Finite-time synchronization of neural networks with interval and distributed time-varying delays via feedback control. (English) Zbl 1482.34131

Summary: This research presents the problem of the finite-time synchronization of neural networks with interval and distributed time-varying delays. A state feedback control is planned for finite-time synchronization of neural networks. By constructing the Lyapunov-Krasovskii functional (LKF) is derived for finite-time stability criteria of neural network systems with interval and continuous differentiable time-varying delays. An extended reciprocally convex matrix inequality, a free-matrix-based integral inequality, Jensen’s inequality and Wirtinger-based integral inequality are used to estimate the upper bound of the derivative of the LKF. The new sufficient finite-time stability conditions have been proposed in the form of linear matrix inequalities. Finally, a numerical example is presented to show the effectiveness of the proposed methods.

MSC:

34D06 Synchronization of solutions to ordinary differential equations
34K20 Stability theory of functional-differential equations
93B52 Feedback control
93C43 Delay control/observation systems
93D40 Finite-time stability
PDFBibTeX XMLCite
Full Text: Link

References:

[1] C. Bishop, Neural Networks for Pattern Recognition, Oxford University Press, Oxford, 1995. · Zbl 0868.68096
[2] L. Chua, L. Yang, Cellular neural networks: Applications, IEEE Trans. Circ. Syst. 35 (1988) 1273-1290.
[3] W. Liu, Z. Wang, X. Liu, N. Zeng, F. Alsaadi, A survey of deep neural network architectures and their applications, Neurocomputing 234 (2017) 11-26.
[4] H. Shao, H. Li, L. Shao, Improved delay-dependent stability result for neural networks with time-varying delays, ISA Tran. 80 (2018) 35-42.
[5] X. Li, S. Song, Stabilization of delay systems: Delay-dependent impulsive control, IEEE Trans. Autom. Control 62 (2017) 406-411. · Zbl 1359.34089
[6] T. Botmart, N. Yotha, K. Mukdasai, S. Wongaree, Global synchronization for hybrid coupled neural networks with interval time-varying delays: A matrix-based quadratic convex approach, Asian-Eur. J. Math. 10 (2017) Article ID 1750025. · Zbl 1370.34101
[7] Y. Du, X. Liu, S. Zhong, Robust reliableH∞control for neural networks with mixed time delays, Chaos Solitons Fractals 91 (2016) 1-8. · Zbl 1372.93095
[8] 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.
[9] Z. Xu, D. Peng, X. Li, Synchronization of chaotic neural networks with time delay via distributed delayed impulsive control, Neural Networks 118 (2019) 332-337. · Zbl 1443.93066
[10] B. Yang, J. Wang, X. Liu, Improved delay-dependent stability criteria for generalized neural networks with time-varying delays, Inform. Sci. 420 (2017) 299-312. · Zbl 1447.34064
[11] X.F. Liu, X. Liu, M. Tang, F. Wang, Improved exponential stability criterion for neural networks with time-varying delay, Neurocomputing 234 (2017) 154-163.
[12] Y. Shi, J. Cao, G. Chen, Exponential stability of complex-valued memristor-based neural networks with time-varying delays, Appl. Math. Comput. 313 (2017) 222-234. · Zbl 1426.92004
[13] Y. He, M.D. Ji, C.K. Zhang, M. Wu, Global exponential stability of neural networks with time-varying delay based on free-matrix-based integral inequality, Neural Networks 77 (2016) 80-86. · Zbl 1417.34174
[14] P. Dorato, Short time stability in linear time-varying system, In: Proc. of the IRE International Convention Record, New York, USA 4 (1961) 83-87.
[15] F. Amato, M. Ariola, C. Cosentino, Finite-time stabilization via dynamic output feedback, Automatica 42 (2006) 337-342. · Zbl 1099.93042
[16] F. Amato, M. Ariola, C. Cosentino, Robust finite-time stabilisation of uncertain linear systems, Int. J. Control 84 (12) (2011) 2117-2127. · Zbl 1236.93121
[17] P. Dorato, Robust finite-time stability design via linear matrix inequalities, Proceeding IEEE Conference on Decision and Control (1997) 1305-1306.
[18] F. Amato, M. Ariola, P. Dorato, Robust finite-time stabilization of linear systems depending on parameter uncertainties, In: Proceeding IEEE Conference on Decision and Control (1999) 1207-1208.
[19] F. Amato, M. Ariola, P. Dorato, Finite-time control of linear systems subject to parametric uncertainties and disturbances, Automatica 37 (2001) 678-682. · Zbl 0983.93060
[20] L. Liu, J. Sun, Finite-time stabilization of linear systems via impulsive control, Int. J. Control 81 (6) (2008) 905-909. · Zbl 1149.93338
[21] D.L. Debeljkovic, S.B. Stojanovic, A.M. Jovanovic, Finite-time stability of continuous time delay systems: Lyapunov-like approach with Jensen’s and Coppel’s inequality, Acta Polytech. Hungarica 10 (7) (2013) 135-150.
[22] T. Rojsiraphisal, J. Puangmalai, An improved finite-time stability and stabilization of linear system with constant delay, Math. Probl. Eng. 2014 (2014) Article ID 154769. · Zbl 1407.93336
[23] S.B. Stojanovic, D.L. Debeljkovic, D.S. Antic, Finite-time stability and stabilization of linear time-delay systems, Facta Univ. Automat. Control Robot. 11 (1) (2012) 25-36.
[24] Z. Zhang, Z. Zhang, H. Zhang, Finite-time stability analysis and stabilization for uncertain continuous-time system with time-varying delay, J. Frankl. Inst. 352 (2015) 1296-1317. · Zbl 1307.93337
[25] X. Lin, K. Liang, H. Li, Y. Jiao, J. Nie, Finite-time stability and stabilization for continuous systems with additive time-varying delays, Circuits Syst. Signal Process 36 (2017) 2971-2990. · Zbl 1371.93152
[26] P. Niamsup, V.N. Phat, Robust finite-time control for linear time-varying delay systems with bounded control, Asian J. Control. 18 (2016) 2317-2324. · Zbl 1354.93044
[27] 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. Simulation 171 (2020) 170—186. · Zbl 1510.93276
[28] S.B. Stojanovic, Further improvement in delay-dependent finite-time stability criteria for uncertain continuous-time systems with time-varying delays, IET Control Theory and Applications 10 (8) (2016) 926-938.
[29] P. Niamsup, K. Ratchagit, V.N. Phat, Novel criteria for finite-time stabilization and guaranteed cost control of delayed neural networks, Neurocomputing 160 (2015) 281-286.
[30] M. Syed Ali, S. Saravanan, Finite-time stability for memristor based switched neural networks with time-varying delays via average dwell time approach, Neurocomputing 275 (2018) 1637-1649.
[31] G. Garcia, S. Tarbouriech, J. Bernussou, Finite-time stabilization of linear timevarying continuous systems, IEEE Trans. Automat. Control 54 (2) (2009) 364-369. · Zbl 1367.93060
[32] T. La-inchua, P. Niamsup, X. Liu, Finite-time stability of large-scale systems with interval time-varying delay in interconnection, Complexity 2017 (2017) Article ID 1972748. · Zbl 1367.93439
[33] M.P. Lazarevic, D.L. Debeljkovic, Z.L. Nenadic, S.A. Milinkovic, Finite-time stability of delayed systems, IMA J. Math. Control Inform. 17 (2) (2000) 101-109. · Zbl 0979.93095
[34] X. Yang, X. Li, Finite-time stability of linear non-autonomous systems with timevarying delays, Adv. Difference Equations 101 (2018). · Zbl 1445.93033
[35] Z.Y. Wu, Q.L. Ye, D.F. Liu, Finite-time synchronization of dynamical networks coupled with complex-variable chaotic systems, Int. J. Mod. Phys. C. 24 (9) (2013) 1350-1358.
[36] H. Shen, J.H. Park, Z.G. Wu, Finite-time synchronization control for uncertain Markov jump neural networks with input constraints, Nonlinear Dynam. 77 (2014) 1709-1720. · Zbl 1331.92019
[37] S. Li, X. Peng, Y. Tang, Y. Shi, Finite-time synchronization of time-delayed neural networks with unknown parameters via adaptive control, Neurocomputing 308 (2018) 65-74.
[38] K.S. Anand, G.A. Harish Babu, M. Syed Ali, S. Padmanabhan, Finite-time synchronization of Markovian jumping complex dynamical networks and hybrid couplings, Neurocomputing 308 (2018) 65-74.
[39] K. Gu, V.L. Kharitonov, J. Chen, Stability of Time-Delay System, Birkhauser, Boston, Massachusetts, 2003. · Zbl 1039.34067
[40] W. Chen, F. Gao, Stability analysis of systems via a new double free-matrix-based integral inequality with interval time-varying delay, Internat. J. Systems Sci. (2019) Article ID 1672118. · Zbl 1483.93462
[41] A. Seuret, F. Gouaisbaut, Wirtinger-based integral inequality: Application to timedelay systems, Automatica 49 (9) (2013) 2860-2866. · Zbl 1364.93740
[42] J. Jiao, R. Zhang, An extended reciprocally convex matrix inequality and its application to stability analysis of systems with additive time-varying delays, J. Franklin Inst. 357 (4) (2020) 2282-2294. · Zbl 1451.93274
[43] N. Zhao, C. Lin, B. Chen, Q.G. Wang, A new double integral inequality and application to stability test for time-delay systems, Appl. Math. Lett. 65 (2017) 26-31 · Zbl 1350.93061
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.