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Exponential synchronization for stochastic neural networks with mixed time delays and Markovian jump parameters via sampled data. (English) Zbl 1406.93304
Summary: The exponential synchronization issue for stochastic neural networks (SNNs) with mixed time delays and Markovian jump parameters using sampled-data controller is investigated. Based on a novel Lyapunov-Krasovskii functional, stochastic analysis theory, and linear matrix inequality (LMI) approach, we derived some novel sufficient conditions that guarantee that the master systems exponentially synchronize with the slave systems. The design method of the desired sampled-data controller is also proposed. To reflect the most dynamical behaviors of the system, both Markovian jump parameters and stochastic disturbance are considered, where stochastic disturbances are given in the form of a Brownian motion. The results obtained in this paper are a little conservative comparing the previous results in the literature. Finally, two numerical examples are given to illustrate the effectiveness of the proposed methods.
MSC:
93E03 Stochastic systems in control theory (general)
68T05 Learning and adaptive systems in artificial intelligence
93C57 Sampled-data control/observation systems
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[1] Wang, Z.; Wang, Y.; Liu, Y., Global synchronization for discrete-time stochastic complex networks with randomly occurred nonlinearities and mixed time delays, IEEE Transactions on Neural Networks, 21, 1, 11-25, (2010)
[2] Wu, H., Global exponential stability of Hopfield neural networks with delays and inverse Lipschitz neuron activations, Nonlinear Analysis: Real World Applications, 10, 4, 2297-2306, (2009) · Zbl 1163.92308
[3] Wu, H.; Yu, H., Global robust exponential stability for Hopfield neural networks with non-Lipschitz activation functions, Nonlinear Oscillations, 15, 1, 127-138, (2012)
[4] Yang, X.; Cao, J.; Lu, J., Synchronization of delayed complex dynamical networks with impulsive and stochastic effects, Nonlinear Analysis: Real World Applications, 12, 4, 2252-2266, (2011) · Zbl 1223.37115
[5] Park, J. H.; Kwon, O. M.; Lee, S. M., LMI optimization approach on stability for delayed neural networks of neutral-type, Applied Mathematics and Computation, 196, 1, 236-244, (2008) · Zbl 1157.34056
[6] Liu, Z.; Zhang, H.; Zhang, Q., Novel stability analysis for recurrent neural networks with multiple delays via line integral-type L-K functional, IEEE Transactions on Neural Networks, 21, 11, 1710-1718, (2010)
[7] Zhang, H.; Liu, Z.; Huang, G.-B.; Wang, Z., Novel weighting-delay-based stability criteria for recurrent neural networks with time-varying delay, IEEE Transactions on Neural Networks, 21, 1, 91-106, (2010)
[8] Wu, H.; Li, N.; Wang, K.; Xu, G.; Guo, Q., Global robust stability of switched interval neural networks with discrete and distributed time-varying delays of neural type, Mathematical Problems in Engineering, 2012, (2012) · Zbl 1264.34145
[9] Wu, H.; Zhang, L., Almost periodic solution for memristive neural networks with time-varying delays, Journal of Applied Mathematics, 2013, (2013) · Zbl 1266.92004
[10] Faydasicok, O.; Arik, S., Equilibrium and stability analysis of delayed neural networks under parameter uncertainties, Applied Mathematics and Computation, 218, 12, 6716-6726, (2012) · Zbl 1245.34075
[11] Huang, T.; Li, C.; Yu, W.; Chen, G., Synchronization of delayed chaotic systems with parameter mismatches by using intermittent linear state feedback, Nonlinearity, 22, 3, 569-584, (2009) · Zbl 1167.34386
[12] Wu, Z.; Shi, P.; Su, H.; Chu, J., Exponential synchronization of neural networks with discrete and distributed delays under time-varying sampling, IEEE Transactions on Neural Networks and Learning Systems, 23, 9, 1368-1376, (2012)
[13] Yang, X.; Cao, J.; Lu, J., Stochastic synchronization of complex networks with nonidentical nodes via hybrid adaptive and impulsive control, IEEE Transactions on Circuits and Systems I, 59, 2, 371-384, (2012)
[14] Gan, Q., Exponential synchronization of stochastic Cohen-Grossberg neural networks with mixed time-varying delays and reaction-diffusion via periodically intermittent control, Neural Networks, 31, 12-21, (2012) · Zbl 1245.93125
[15] Zhang, W.; Fang, J.; Miao, Q.; Chen, L.; Zhu, W., Synchronization of Markovian jump genetic oscillators with nonidentical feedback delay, Neurocomputing, 101, 347-353, (2013)
[16] Wu, H.; Guo, X.; Ding, S.; Wang, L.; Zhang, L., Exponential synchronization for switched coupled neural networks via intermittent control, Journal of Computer Information Systems, 9, 9, 3503-3510, (2013)
[17] Zhang, H.; Ma, T.; Huang, G.-B.; Wang, C., Robust global exponential synchronization of uncertain chaotic delayed neural networks via dual-stage impulsive control, IEEE Transactions on Systems, Man, and Cybernetics B, 40, 3, 831-844, (2010)
[18] Wang, Y.; Wang, Z.; Liang, J.; Li, Y.; Du, M., Synchronization of stochastic genetic oscillator networks with time delays and Markovian jumping parameters, Neurocomputing, 73, 13–15, 2532-2539, (2010)
[19] Yang, X.; Cao, J.; Lu, J., Synchronization of randomly coupled neural networks with Markovian jumping and time-delay, IEEE Transactions on Circuits and Systems I, 60, 2, 363-376, (2013)
[20] Tian, J.; Li, Y.; Zhao, J.; Zhong, S., Delay-dependent stochastic stability criteria for Markovian jumping neural networks with mode-dependent time-varying delays and partially known transition rates, Applied Mathematics and Computation, 218, 9, 5769-5781, (2012) · Zbl 1248.34123
[21] Yu, J.; Sun, G., Robust stabilization of stochastic Markovian jumping dynamical networks with mixed delays, Neurocomputing, 86, 107-115, (2012)
[22] Zhang, D.; Yu, L., Exponential state estimation for Markovian jumping neural networks with time-varying discrete and distributed delays, Neural Networks, 35, 103-111, (2012) · Zbl 1382.93031
[23] Sheng, L.; Yang, H., Robust stability of uncertain Markovian jumping Cohen-Grossberg neural networks with mixed time-varying delays, Chaos, Solitons & Fractals, 42, 4, 2120-2128, (2009) · Zbl 1198.93166
[24] Balasubramaniam, P.; Lakshmanan, S., Delay-range dependent stability criteria for neural networks with Markovian jumping parameters, Nonlinear Analysis: Hybrid Systems, 3, 4, 749-756, (2009) · Zbl 1175.93206
[25] Zheng, C.-D.; Zhou, F.; Wang, Z., Stochastic exponential synchronization of jumping chaotic neural networks with mixed delays, Communications in Nonlinear Science and Numerical Simulation, 17, 3, 1273-1291, (2012) · Zbl 1239.93115
[26] Li, Y.; Zhu, Y.; Zeng, N.; Du, M., Stability analysis of standard genetic regulatory networks with time-varying delays and stochastic perturbations, Neurocomputing, 74, 17, 3235-3241, (2011)
[27] Pan, L.; Cao, J., Stochastic quasi-synchronization for delayed dynamical networks via intermittent control, Communications in Nonlinear Science and Numerical Simulation, 17, 3, 1332-1343, (2012) · Zbl 1239.93114
[28] Zhu, Q.; Cao, J., Exponential stability of stochastic neural networks with both Markovian jump parameters and mixed time delays, IEEE Transactions on Systems, Man, and Cybernetics B, 41, 2, 341-353, (2011)
[29] Fu, J.; Zhang, H.; Ma, T.; Zhang, Q., On passivity analysis for stochastic neural networks with interval time-varying delay, Neurocomputing, 73, 4–6, 795-801, (2010)
[30] Zhang, H.; Wang, Y., Stability analysis of Markovian jumping stochastic Cohen-Grossberg neural networks with mixed time delays, IEEE Transactions on Neural Networks, 19, 2, 366-370, (2008)
[31] Liu, Y.; Wang, Z.; Liang, J.; Liu, X., Synchronization and state estimation for discrete-time complex networks with distributed delays, IEEE Transactions on Systems, Man, and Cybernetics B, 38, 5, 1314-1325, (2008)
[32] Allegretto, W.; Papini, D.; Forti, M., Common asymptotic behavior of solutions and almost periodicity for discontinuous, delayed, and impulsive neural networks, IEEE Transactions on Neural Networks, 21, 7, 1110-1125, (2010)
[33] Wang, Z.; Liu, Y.; Liu, X., State estimation for jumping recurrent neural networks with discrete and distributed delays, Neural Networks, 22, 1, 41-48, (2009) · Zbl 1335.93125
[34] Huang, H.; Huang, T.; Chen, X., Global exponential estimates of delayed stochastic neural networks with Markovian switching, Neural Networks, 36, 136-145, (2012) · Zbl 1258.93097
[35] Huang, T.; Li, C.; Duan, S.; Starzyk, J., Robust exponential stability of uncertin delayed neural networks with stochastic perturbation and impulse effects, IEEE Transactions on Neural Networks and Learning Systems, 23, 6, 866-875, (2012)
[36] Wu, Z.-G.; Park, J. H.; Su, H.; Chu, J., Discontinuous Lyapunov functional approach to synchronization of time-delay neural networks using sampled-data, Nonlinear Dynamics, 69, 4, 2021-2030, (2012) · Zbl 1263.34075
[37] Theesar, S. J. S.; Banerjee, S.; Balasubramaniam, P., Synchronization of chaotic systems under sampled-data control, Nonlinear Dynamics, 70, 3, 1977-1987, (2012) · Zbl 1268.93074
[38] Wu, Z. G.; Shi, P.; Su, H.; Chu, J., Stochastic synchronization of Markovian jump neural networks with time-varying delay using sampled data, IEEE Transactions on Cybernetics, 43, 6, 1796-1806, (2013)
[39] Zhang, Y.; Han, Q.-L., Network-based synchronization of delayed neural networks, IEEE Transactions on Circuits and Systems I, 60, 3, 676-689, (2013)
[40] Li, H.; Chen, B.; Zhou, Q.; Qian, W., Robust stability for uncertain delayed fuzzy Hopfield neural networks with Markovian jumping parameters, IEEE Transactions on Systems, Man, and Cybernetics B, 39, 1, 94-102, (2009)
[41] Shu, Z.; Lam, J., Exponential estimates and stabilization of uncertain singular systems with discrete and distributed delays, International Journal of Control, 81, 6, 865-882, (2008) · Zbl 1152.93462
[42] Zhang, X.-M.; Han, Q.-L., Stability of linear systems with interval time-varying delays arising from networked control systems, Proceeding of the 36th Annual Conference of the IEEE Industrial Electronics Society (IECON ’10)
[43] Park, P.; Ko, J. W.; Jeong, C., Reciprocally convex approach to stability of systems with time-varying delays, Automatica, 47, 1, 235-238, (2011) · Zbl 1209.93076
[44] He, Y.; Liu, G.; Rees, D., New delay-dependent stability criteria for neural networks with yime-varying delay, IEEE Transactions on Neural Networks, 18, 1, 310-314, (2007)
[45] Wang, Z.; Liu, Y.; Yu, L.; Liu, X., Exponential stability of delayed recurrent neural networks with Markovian jumping parameters, Physics Letters A, 356, 4-5, 346-352, (2006) · Zbl 1160.37439
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