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Synchronisation of discrete-time complex networks with randomly occurring uncertainties, nonlinearities and time-delays

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  • L. Jarina Banu
  • P. Balasubramaniam

Abstract

This paper deals with the synchronisation problem for an array of coupled complex discrete-time networks with the presence of randomly occurring information. The time-varying delays, parameter uncertainties and nonlinearities enter into the system in a random way and such randomly occurring time-delays, randomly occurring uncertainties and randomly occurring sector-like nonlinearities obey certain mutually uncorrelated Bernoulli-distributed white-noise sequences. By employing direct delay decomposition approach and constructing suitable Lyapunov–Krasovskii functional, sufficient conditions are established to ensure the synchronisation criteria for the complex networks with randomly occurring information in terms of linear matrix inequalities. Finally, in numerical examples, synchronisation of Barabàsi Albert scale-free networks and chaotic synchronisation of Lorenz system are rendered to exemplify the effectiveness and applicability of the proposed results.

Suggested Citation

  • L. Jarina Banu & P. Balasubramaniam, 2014. "Synchronisation of discrete-time complex networks with randomly occurring uncertainties, nonlinearities and time-delays," International Journal of Systems Science, Taylor & Francis Journals, vol. 45(7), pages 1427-1450, July.
    • Handle: RePEc:taf:tsysxx:v:45:y:2014:i:7:p:1427-1450
    DOI: 10.1080/00207721.2013.844287
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    References listed on IDEAS

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    1. J. H. Park & S. M. Lee & H. Y. Jung, 2009. "LMI Optimization Approach to Synchronization of Stochastic Delayed Discrete-Time Complex Networks," Journal of Optimization Theory and Applications, Springer, vol. 143(2), pages 357-367, November.
    2. Yisha Liu & Zidong Wang & Wei Wang, 2011. "Reliable control for discrete uncertain time-delay systems with randomly occurring nonlinearities: the output feedback case," International Journal of Systems Science, Taylor & Francis Journals, vol. 42(5), pages 809-820.
    3. Steven H. Strogatz, 2001. "Exploring complex networks," Nature, Nature, vol. 410(6825), pages 268-276, March.
    4. Li, Chunguang & Chen, Guanrong, 2004. "Synchronization in general complex dynamical networks with coupling delays," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 343(C), pages 263-278.
    5. Barabási, Albert-László & Albert, Réka & Jeong, Hawoong, 1999. "Mean-field theory for scale-free random networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 272(1), pages 173-187.
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