Abstract
This article discusses the synchronization problem of singular neutral complex dynamical networks (SNCDN) with distributed delay and Markovian jump parameters via pinning control. Pinning control strategies are designed to make the singular neutral complex networks synchronized. Some delay-dependent synchronization criteria are derived in the form of linear matrix inequalities based on a modified Lyapunov-Krasovskii functional approach. By applying the Lyapunov stability theory, Jensen’s inequality, Schur complement, and linear matrix inequality technique, some new delay-dependent conditions are derived to guarantee the stability of the system. Finally, numerical examples are presented to illustrate the effectiveness of the obtained results.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Gong D, Zhang H, Wang Z, Liu J. Synchronization analysis for complex networks with coupling delay based on T-S fuzzy theory. Appl Math Model, 2012, 36: 6215–6224
Ji D H, Park J H, Yoo W J, Won S C, Lee S M. Synchronization criterion for Lur’e type complex dynamical networks with time-varying delay. Phys Lett A, 2010, 374: 1218–1227
Shen H, Park J H, Wu Z G, Zhan Z. Finite-time H∞ synchronization for complex networks with semi-Markov jump topology. Commun Nonlinear Sci Numer Simul, 2014, 24: 40–51
Cai S, Hao J, He Q, Liu Z. Exponenial synchronization of complex delayed dynamical networks via pinning periodically intermittent control. Phys Lett A, 2011, 375: 1965–1971
Wang J, Zhang H, Wang B. Local exponential synchronization in complex dynamical networks with time-varying delay and hybrid coupling. Appl Math Comput, 2013, 225: 16–32
Shen H, Wu Z G, Zhang Z, Park J H. Non-fragile mixed H1/l2 - l1 synchronization control for complex networks with Markov jumping-switching topology under unreliable communication links. IET Control Theory and Applications, 2014, 8: 2207–2218
Park M J, Kwon O M, Park J H, Lee S M, Cha E J. Synchronization criteria of fuzzy complex dynamical networks with interval time-varying delays. Appl Math Comput, 2012, 218: 11634–11647
Zhou J, Wu Q, Xiang L. Impulsive pinning complex dynamical networks and applications to firing neuronal synchronization. Nonlinear Dyn Syst Theory, 2012, 69: 1393–403
Wang M, Wang X, Liu Z. A new complex network model with hierarchical and modular structures. Chinese J Phys, 2010, 48: 805–813
Yi J W, Wang Y W, Xiao J W, Huang Y. Exponential synchronization of complex dynamical networks with Markovian jumping parameters and stochastic delays and its application to multi-agent systems. Commun Nonlinear Sci Numer Simul, 2013, 18: 1175–1192
Chen X, Song Q. Global stability of complex-valued neural networks with both leakage time delay and discrete time delay on time scales. Neurocomputing, 2013, 121: 254–264
Huang B, Zhang H, Gong D, Wang J. Synchronization analysis for static neural networks with hybrid couplings and time delays. Neurocomputing, 2015, 148: 288–293
Li H. H1 cluster synchronization and state estimation for complex dynamical networks with mixed time delays. Appl Math Model, 2013, 37: 7223–7244
Balasubramaniam P, Ali M Syed, Arik S. Global asymptotic stability of stochastic fuzzy cellular neural networks with multiple time-varying delays. Expert Systems with Applications, 2010, 37: 7737–7744
Ali M Syed. Stability of Markovian jumping recurrent neural networks with discrete and distributed time- varying delays. Neurocomputing, 2015, 149: 1280–1285
Ali M Syed, Arik S, Saravanakumar R. Delay-dependent stability criteria of uncertain Markovian jump neural networks with discrete interval and distributed time-varying delays. Neurocomputing, 2015, 158: 167–173
Lee T H, Wu Z G, Park J H. Synchronization of a complex dynamical network with coupling time-varying delays via sampled-data control. Appl Math Comput, 2012, 219: 1354–1366
Song Q. Synchronization analysis in an array of asymmetric neural networks with time-varying delays and nonlinear coupling. Appl Math Comput, 2010, 216: 1605–1613
Yang X, Cao J, Yang Z. Synchronization of coupled reaction-diffusion neural networks with time-varying delays via pinning-impulsive controller. SIAM J Control Optim, 2013, 51: 3486–3510
Wang G, Yin Q, Shen Y, Jiang F. H1 synchronization of directed complex dynamical networks with mixed time-delays and switching structures. Circuits Syst Signal Process, 2013, 32: 1575–1593
Zheng S, Wang S, Dong G, Bi Q. Adaptive synchronization of two nonlinearly coupled complex dynamical networks with delayed coupling. Commun Nonlinear Sci Numer Simul, 2012, 17: 284–291
Li H. New criteria for synchronization stability of continuous complex dynamical networks with non-delayed and delayed coupling. Commun Nonlinear Sci Numer Simul, 2011, 16: 1027–1043
Nian F, Wang X. Chaotic synchronization of hybrid state on complex networks. Int J Mod Phys C, 2010, 21: 457–469
Guo W, Austin F, Chen S. Global synchronization of nonlinearly coupled complex networks with non-delayed coupling. Commun Nonlinear Sci Numer Simul, 2010, 15: 1631–1639
Yu W, Chen G, Cao J. Adaptive synchronization of uncertain coupled stochastic complex networks. Asian J Cont, 2011, 13: 418–429
Dua H, Shi P, Lua N. Function projective synchronization in complex dynamical networks with time delay via hybrid feedback control. Nonlinear Anal Real World Appl, 2013, 14: 1182–1190
Hu A, Cao J, Yang Z. Cluster synchronization in directed networks of non-identical systems with noises via random pinning control. Phys A, 2014, 395: 537–548
Li L, Cao J. Cluster synchronization in an array of coupled stochastic delayed neural networks via pinning 886 ACTA MATHEMATICA SCIENTIA Vol.40 Ser.B control. Neurocomputing, 2011, 74: 846–856
Yu W, Chen G, Lu J. On pinning synchronization of complex dynamical networks. Automatica, 2009, 45: 429–435
Song Q, Cao J. On pinning synchronization of directed and undirected complex dynamical networks. IEEE Trans Circuits Syst I, Reg Papers, 2010, 57: 672–680
Jin X Z, Yang G H. Adaptive synchronization of a class of uncertain complex networks against netwotk deterioration. IEEE Trans Circuits Syst I, Reg Papers, 2011, 58: 1369–1409
Wang Z, Huang L, Wang Y, Zuo Y. Synchronization analysis of networks with both delayed and non-delayed couplings via adaptive pinning control method. Commun Nonlinear Sci Numer Simul, 2010, 15: 4202–4208
Feng J, Sun S, Xu C, Zhao Y, Wang J. The synchronization of general complex dynamical network via pinning control. Nonlinear Dyn, 2012, 67: 1623–1633
Zhang Y, Zhang Q, Yan X G. Complex dynamics in a singular Leslieower predatorprey bioeconomic model with time delay and stochastic. Physica A, 2014, 404: 180–191
Wu S L, Li C X. On semi-convergence of modified HSS method for a class of complex singular linear systems. Appl Math Lett, 2014, 38: 57–60
Ma Y, Zheng Y. Synchronization of continuous-time Markovian jumping singular complex networks with mixed mode-dependent time delays. Neurocomputing, 2015, 156: 52–59
Koo J H, Ji D H, Won S C. Synchronization of singular complex dynamic networks with time-varying delays. Appl Math Comput, 2010, 217: 3916–3923
Duan W, Cai C, Zou Y, You J. Synchronization criteria for singular complex dynamical networks with delayed coupling and non-delayed coupling. Control Theory Appl, 2013, 30(8): 947–955
Zeng J, Cao J. Synchronization in singular hybrid complex networks with delayed coupling. Internat J Systems Control and Communications, 2011, 3: 144–157
Yang M, Wang Y, Xiao J, Huang Y. Robust synchronization of singular complex switched networks with parametric uncertainties and unknown coupling topologies via impulsive control. Commun Nonlinear Sci Numer Simul, 2012, 17(11): 4404–4416
Li H, Ning Z, Yin Y, Tang Y. Synchronization and state estimation for singular complex dynamical networks with time-varying delays. Commun Nonlinear Sci Numer Simul, 2013, 18: 194–208
Koo J H, Ji D H, Won S C. Synchronization of singular complex dynamical networks with time-varying delays. Appl Math Comput, 2010, 217: 3916–3923
Liu Z Y, Lin C, Chen B. A neutral system approach to stability of singular time-delay systems. J Franklin Inst, 2014, 351: 4939–4948
Ji D H, Lee D W, Koo J H, et al. Synchronization of neutral complex dynamical networks with coupling Time-varying delays. Non Linear Dyn, 2011, 65: 349–358
Liu X, Xi H. Synchronization of neutral complex dynamical network with Markovian switching based on sampled-data controller. Neurocomputing, 2014, 139: 163–179
Li H, Yue D. Synchronization of Markovian jumping stochastic complex networks with distributed time delays and probabilistic interval discrete time-varying delays. J Phys A Math Theor, 2010, 43: 105–101
Yang X, Cao J. Finite-time stochastic synchronization of complex networks. Appl Math Model, 2010, 34: 3631–3641
Sun Y, Li W, Ruan J. Generalized outer synchronization between complex dynamical networks with time delay and noise perturbation. Commun Nonlinear Sci Numer Simul, 2013, 18: 989–998
Wu Z G, Shi P, Su H, Chu J. Sampled-data exponential synchronization of complex dynamical networks with time-varying coupling delay. Neural Netw Learn Syst, 2013, 24: 1177–1187
Duan W, Du B, You J, Zou Y. Synchronization criteria for neutral complex dynamic networks with interal Time-varying coupling delays. Asian J Cont, 2013, 15: 1385–1396
Dai L, Singular control systems. Germany: Springer-Verlang, 1989
Masubuchi I, Kamitance Y, Ohara A, Suda N. H∞ control for descriptor systems: A matrix inequalities approach. Utomatica, 1997, 33: 669–673
Gu K, Kharitonov V L, Chen J. Stability of time delay systems. Boston: Birkhuser, 2003
Author information
Authors and Affiliations
Corresponding author
Additional information
The work of author was supported by NBHM grant. 2/48 (5)/2016/NBHMR.P)/- R -D II/ 14088
Electronic supplementary material
Rights and permissions
About this article
Cite this article
Anand, K.S., Yogambigai, J., Harish Babu, G.A. et al. Synchronization of Singular Markovian Jumping Neutral Complex Dynamical Networks with Time-Varying Delays via Pinning Control. Acta Math Sci 40, 863–886 (2020). https://doi.org/10.1007/s10473-020-0319-y
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10473-020-0319-y