Linear matrix inequality approach for synchronization of chaotic fuzzy cellular neural networks with discrete and unbounded distributed delays based on\ sampled-data control

Document Type : Research Paper

Authors

1 Department of Mathematics, Gandhigram Rural Institute - Deemed University, Gandhigram - 624 302, Tamilnadu, India

2 Institute of Mathematical Sciences, Faculty of Science, University of Malaya - 50603, Kuala Lumpur, Malaysia

Abstract

In this paper, linear matrix inequality (LMI) approach for synchronization of chaotic fuzzy cellular neural networks (FCNNs) with discrete and unbounded distributed delays based on sampled-data control
is investigated. Lyapunov-Krasovskii functional combining with the input delay approach as well as the free-weighting matrix approach are employed to derive several sufficient criteria in terms of LMIs ensuring the delayed FCNNs to be asymptotically synchronous. The restriction such as the time-varying delay required to be differentiable or even its time-derivative assumed to be smaller than one, are removed. Instead, the time-varying delay is only assumed to be bounded. Finally, numerical examples and its simulations are provided to demonstrate the effectiveness of the derived results.

Keywords


[1] A. Arunkumar, R. Sakthivel, K. Mathiyalagan and S. Marshal Anthoni, Robust state estimation
for discrete-time BAM neural networks with time-varying delay, Neurocomputing, 131
(2014), 171-178.
[2] A. Arunkumar, R. Sakthivel, K. Mathiyalagan and Ju H. Park, Robust stochastic stability
of discrete-time fuzzy Markovian jump neural networks, ISA Transactions, 53 (2014), 1006–
1014.
[3] P. Balasubramaniam, M. Kalpana and R. Rakkiyappan, Linear matrix inequality approach
for synchronization control of fuzzy cellular neural networks with mixed time delays, Chinese
Physics B, 21 (2012): 048402.
[4] S. Boyd, L. E. Ghaoui, E. Feron and V. Balakrishnan, Linear Matrix Inequalities in Systems
and Control Theory (SIAM, Philadelphia, 1994).
[5] T. L. Carroll and L. M. Pecora, Synchronization chaotic circuits, IEEE Trans. Circuits Syst.,
38 (1991), 453–456.
[6] L. O. Chua and L. Yang, Cellular neural networks: theory, IEEE Trans. Circuits Syst., 35
(1988), 1257-1272.
[7] L. O. Chua and L. Yang, Cellular neural networks: applications, IEEE Trans. Circuits Syst.,
35 (1988), 1273-1290.
[8] X. Feng, F. Zhang and W. Wang, Global exponential synchronization of delayed fuzzy cellular
neural networks with impulsive effects, Chaos Solitons Fractals., 44 (2011), 9–16.
[9] T. Feuring, J. J. Buckley, W. M. Lippe and A. Tenhagen, Stability analysis of neural net
controllers using fuzzy neural networks, Fuzzy Sets and Systems, 101 (1999), 303–313.
[10] E. Fridman, A. Seuret and J. P. Richard, Robust sampled-data stabilization of linear systems:
an input delay approach, Automatica, 40 (2004), 1441–1446.
[11] Q. Gan and Y. Liang, Synchronization of chaotic neural networks with time delay in the
leakage term and parametric uncertainties based on sampled-data control, J. Franklin Inst.,
349 (2012), 1955–1971.
[12] Q. Gan, R. Xu and P. Yang, Synchronization of non-identical chaotic delayed fuzzy cellular
neural networks based on sliding mode control, Commun. Nonlinear Sci. Numer. Simul., 17
(2012), 433–443.
[13] Q. Gan, R. Xu and P. Yang, Exponential synchronization of stochastic fuzzy cellular neural
networks with time delay in the leakage term and reaction-diffusion, Commun. Nonlinear Sci.
Numer. Simul., 17 (2012), 1862–1870.
[14] K. Gu, An integral inequality in the stability problem of time-delay systems, in Proceedings
of the 39th IEEE Conference on Decision and Control Sydney, Australia (2000), 2805–2810.
[15] S. Lee, V. Kapila, M. Porfiri and A. Panda, Master-slave synchronization of continuously
and intermittently coupled sampled-data chaotic oscillators, Commun. Nonlinear Sci. Numer.
Simul., 15 (2010), 4100–4113.
[16] T. Li, S. Fei and Q. Zhu, Design of exponential state estimator for neural networks with
distributed delays, Nonlinear Anal. Real World Appl., 10 (2009), 1229–1242.
[17] N. Li, Y. Zhang, J. Hu and Z. Nie, Synchronization for general complex dynamical networks
with sampled-data, Neurocomputing, 74 (2011), 805–811.
[18] Z. Liu, H. Zhang and Z. Wang, Novel stability criterions of a new fuzzy cellular neural
networks with time-varying delays, Neurocomputing, 72 (2009), 1056–1064.
[19] J. Lu and D. J. Hill, Global asymptotical synchronization of chaotic Lur’e systems using
sampled data: a linear matrix inequality approach, IEEE Trans. Circuits Syst. II, 55 (2008),
586–590.
[20] K. Mathiyalagan, S. Hongye and R. Sakthivel, Robust stochastic stability of discrete-time
Markovian jump neural networks with leakage delay, Zeitschrift Fur Naturforschung Section
A-A Journal of Physical Sciences, 69 (2014), 70–80.
[21] K. Mathiyalagan, R. Sakthivel and S. Hongye, Exponential state estimation for discretetime
switched genetic regulatory networks with random delays, Canad. J. Phys., 92 (2014),
976–986.
[22] L. M. Pecora and T. L. Carroll, Synchronization in chaotic systems, Phys. Rev. Lett., 64
(1990), 821–824.
[23] L. M. Pecora, T. L. Carroll, G. A. Johnson, D. J. Mar and J. F. Heagy, Fundamentals of
synchronization in chaotic systems, concepts, and applications, Chaos, 7 (1997), 520–543.
[24] Y. Ping and L. Teng, Exponential synchronization of fuzzy cellular neural networks with
mixed delays and general boundary conditions, Commun. Nonlinear Sci. Numer. Simul., 17
(2012), 1003–1011.
[25] R. Sakthivel, R. Raja and S. Marshal Anthoni, Linear matrix inequality approach to stochastic
stability of uncertain delayed BAM neural networks, IMA J Appl Math., 78 (2013), 1156–
1178.
[26] E. N. Sanchez and J. P. Perez, Input-to-state stability (ISS) analysis for dynamic neural
networks, IEEE Trans. Circuits Syst. I, 46 (1999), 1395-1398.
[27] F. O. Souza, R. M. Palhares and P. Y. Ekel, Asymptotic stability analysis in uncertain multidelayed
state neural networks via Lyapunov-Krasovskii theory, Math. Comput. Modelling, 45
(2007), 1350–1362.
[28] F. O. Souza, R. M. Palhares and P. Y. Ekel, Novel stability criteria for uncertain delayed
Cohen-Grossberg neural networks using discretized Lyapunov functional, Chaos Solitons Fractals,
41 (2009), 2387–2393.
[29] F. O. Souza, R. M. Palhares and P. Y. Ekel, Improved asymptotic stability analysis for
uncertain delayed state neural networks, Chaos Solitons Fractals, 39 (2009), 240–247.
[30] Y. Tang and J. Fang, Robust synchronization in an array of fuzzy delayed cellular neural
networks with stochastically hybrid coupling, Neurocomputing, 72 (2009), 3253–3262.
[31] T. Yang and L. B. Yang, Global stability of fuzzy cellular neural network, IEEE Trans. Circuits
Syst. I, 43 (1996), 880–883.
[32] T. Yang, L. B. Yang, C. W. Wu and L. O. Chua, Fuzzy cellular neural networks: Theory,
in Proceedings of the IEEE International Workshop on Cellular Neural Networks and
Applications, (1996), 181–186.
[33] T. Yang, L. B. Yang, C. W. Wu and L. O. Chua, Fuzzy cellular neural networks: Applications,
in Proceedings of the IEEE International Workshop on Cellular Neural Networks and
Applications, (1996), 225–230.
[34] J. Yu, C. Hu, H. Jiang and Z. Teng, Exponential lag synchronization for delayed fuzzy cellular
neural networks via periodically intermittent control, Math. Comput. Simulation, 82 (2012),
895–908.
[35] F. Yu and H. Jiang, Global exponential synchronization of fuzzy cellular neural networks with
delays and reaction-diffusion terms, Neurocomputing, 74 (2011), 509–515.
[36] L. A. Zadeh, Fuzzy Sets, Information and Control, 8 (1965), 338–353.
[37] C. Zhang, Y. He and M. Wu, Exponential synchronization of neural networks with timevarying
mixed delays and sampled-data, Neurocomputing, 74 (2010), 265–273.