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LMI Optimization Approach to Synchronization of Stochastic Delayed Discrete-Time Complex Networks

Author

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  • J. H. Park

    (Yeungnam University)

  • S. M. Lee

    (Daegu University)

  • H. Y. Jung

    (Yeungnam University)

Abstract

Complex networks are widespread in real-world systems of engineering, physics, biology, and sociology. This paper is concerned with the problem of synchronization for stochastic discrete-time drive-response networks. A dynamic feedback controller has been proposed to achieve the goal of the paper. Then, based on the Lyapunov second method and LMI (linear matrix inequality) optimization approach, a delay-independent stability criterion is established that guarantees the asymptotical mean-square synchronization of two identical delayed networks with stochastic disturbances. The criterion is expressed in terms of LMIs, which can be easily solved by various convex optimization algorithms. Finally, two numerical examples are given to illustrate the proposed method.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joptap:v:143:y:2009:i:2:d:10.1007_s10957-009-9562-z
    DOI: 10.1007/s10957-009-9562-z
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    References listed on IDEAS

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    1. J. H. Park & S. Won, 1999. "Asymptotic Stability of Neutral Systems with Multiple Delays," Journal of Optimization Theory and Applications, Springer, vol. 103(1), pages 183-200, October.
    2. J. H. Park, 2001. "Robust Stabilization for Dynamic Systems with Multiple Time-Varying Delays and Nonlinear Uncertainties," Journal of Optimization Theory and Applications, Springer, vol. 108(1), pages 155-174, January.
    3. Park, Ju H., 2006. "A novel criterion for global asymptotic stability of BAM neural networks with time delays," Chaos, Solitons & Fractals, Elsevier, vol. 29(2), pages 446-453.
    4. Lü, Jinhu & Yu, Xinghuo & Chen, Guanrong, 2004. "Chaos synchronization of general complex dynamical networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 334(1), pages 281-302.
    5. Park, Ju H., 2006. "On global stability criterion for neural networks with discrete and distributed delays," Chaos, Solitons & Fractals, Elsevier, vol. 30(4), pages 897-902.
    6. J. H. Park, 2005. "Convex Optimization Approach to Dynamic Output Feedback Control for Delay Differential Systems of Neutral Type," Journal of Optimization Theory and Applications, Springer, vol. 127(2), pages 411-423, November.
    7. J. H. Park, 2004. "On Dynamic Output Feedback Guaranteed Cost Control of Uncertain Discrete-Delay Systems: LMI Optimization Approach," Journal of Optimization Theory and Applications, Springer, vol. 121(1), pages 147-162, April.
    8. 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.
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    Cited by:

    1. 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.

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