Abstract
This paper is further to investigate the global synchronization of the cellular neural networks with both multi-delays and distributed delays. Based on the Lyapunov stability theorem, by using the LMI technique and designing a sliding mode control (SMC) approach, a less conservative yet sufficient condition is derived to guarantee the global stability of the error system with both delay-independent and delay-dependent situations. The feasible SMC law is designed such that the trajectory of the error system is globally driven onto the specified sliding surface. The global synchronization is obtained at last.
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References
Chua, L.O., Yang, L.: Cellular Neural Networks: Theory. IEEE Trans. Circuits Syst. I. 35, 1257–1272 (1998)
Singh, V.: A Generalized LMI-based Approach to the Global Asymptotic Stability of Delayed Cellular Neural Networks. IEEE Trans. Neural Netw. 15, 223–225 (2004)
Chen, A.P., Cao, J.D., Huang, L.H.: Global Robust Stability of Interval Cellular Neural Networks With Time-varying Delays. Chaos Solitons Fractals 23, 787–799 (2005)
Huang, L.H., Huang, C.X., Liu, B.W.: Dynamics of a Class of Cellular Neural Networks With Time-varying Delays. Phys. Lett. A. 345, 330–344 (2005)
Hu, S.Q., Liu, D.R.: On the global output convergence of a class of recurrent neural networks with time-varying inputs. Neural Netw. 18, 171–178 (2005)
Wang, Z., Liu, Y., Liu, X.: Stability Analysis for Stochastic Cohen-Grossberg Neural Networks with Mixed Time Delays. IEEE Trans. Neural Netw. 17, 814–820 (2006)
Dai, L.M., Wang, G.Q.: Implementation of Periodicity Ratio in Analyzing Nonlinear Dynamic Systems: A Comparison With Lyapunov Exponent. J. Compu. Nonli. Dyn. 3(1), 011006 (2008)
Cai, G.L., Yao, Q., Shao, H.J.: Global synchronization of weighted cellular neural networks with time-varying coupling delays. Commun. Nonlinear Sci. Numer. Simul. (2012), doi:10.1016/j.cnsns.2012.02.010
Liu, D.R., Xiong, X.X.: Identification of motifs with insertions and deletions in protein sequences using self-organizing neural networks. Neural Netw. 18, 8355–8842 (2005)
Jiang, H.J., Teng, Z.D.: A New Criterion on the Global Exponential Stability for Cellular Neural Networks With Multiple Time-varying Delays. Phys. Lett. A. 338, 461–471 (2005)
Gau, R.S., Lien, C.H., Hsieh, J.G.: Global Exponential Stability for Uncertain Cellular Neural Networks With Multiple Time-varying Delays via LMI Approach. Chaos Solitons Fractals 32, 1258–1267 (2007)
Ma, K.Y., Yu, L., Zhang, W.A.: Global Exponential Stability of Cellular Neural Networks With Time-varying Discrete and Distributed Delays. Neurocomputing 72, 2705–2709 (2009)
Zhang, Q., Wei, X.P., Xu, J.: Delay-dependent Exponential Stability of Cellular Neural Networks With Time-varying Delays. Chaos Solitons Fractals 23, 1363–1369 (2005)
He, Y., Liu, G.P., Rees, D.: New Delay-dependent Stability Criteria for Neural Networks With Time-varying Delay. IEEE Trans. Neural Netw. 18, 310–314 (2007)
Cai, G.L., Shao, H.J., Yao, Q.: A Linear Matrix Inequality Approach to Global Synchronization of Multi-Delay Hopeld Neural Networks with Parameter Perturbations. Chin. J. Phys. 50, 86–99 (2012)
Mou, S., Gao, H., Lam, J., Qiang, W.: A New Criterion of Delaydependent Asymptotic Stability for Hopfield Neural Networks With Time Delay. IEEE Trans. Neural. Netw. 19, 532–535 (2008)
Wang, D., Liu, D.R., Wei, Q.L.: Finite-horizon neuro-optimal tracking control for a class of discrete-time nonlinear systems using adaptive dynamic programming approach. Neurocomputing 78, 14–22 (2012)
Zhang, Q., Wei, X.P., Xu, J.: Delay-dependent Exponential Stability Criteria for Non-autonomous Cellular Neural Networks With Time-varying Delays. Chaos Solitons Fractals 36, 985–990 (2008)
Huang, H., Feng, G.: Synchronization of Nonidentical Chaotic Neural Networks with Time Delays. Neural Netw. 22, 869–874 (2009)
Shao, H.J., Cai, G.L., Wang, H.X.: A Linear Matrix Inequality Approach to Global Synchronisation of Non-parameters Perturbations of Multi-delay Hopfield Neural Network. Chin. Phys. B. 19, 110509.1–110509.6 (2010)
Gan, Q.T., Xu, R., Kang, X.B.: Synchronization of Chaotic Neural Networks with Mixed Time Delays. Commun. Nonlinear Sci. Numer. Simul. 16, 966–974 (2011)
Cao, J.D., Lu, J.Q.: Adaptive Synchronization of Neural Networks With or Without Time-varying Delays. Chaos 16, 013133 (2006)
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Cai, G., Yao, Q., Wu, X. (2012). The SMC Approach to Global Synchronization of the Cellular Neural Networks with Multi-delays and Distributed Delays. In: Wang, J., Yen, G.G., Polycarpou, M.M. (eds) Advances in Neural Networks – ISNN 2012. ISNN 2012. Lecture Notes in Computer Science, vol 7367. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31346-2_27
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DOI: https://doi.org/10.1007/978-3-642-31346-2_27
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