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Robust \(\mathcal{H}_{\infty}\) decentralized dynamic control for synchronization of a complex dynamical network with randomly occurring uncertainties

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Abstract

This paper considers synchronization problem of an uncertain complex dynamical network. The norm-bounded uncertainties enter into the complex dynamical network in randomly ways, and such randomly occurring uncertainties (ROUs) obey certain mutually uncorrelated Bernoulli distributed white noise sequences. Under the circumstances, a robust \(\mathcal{H}_{\infty}\) decentralized dynamic feedback controller is designed to achieve asymptotic synchronization of the network. Based on Lyapunov stability theory and linear matrix inequality (LMI) framework, the existence condition for feasible controllers is derived in terms of LMIs. Finally, the proposed method is applied to a numerical example in order to show the effectiveness of our result.

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Acknowledgements

This work was supported in part by MEST & DGIST (12-BD-0101, Renewable energy and intelligent robot convergence technology development.)

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Authors and Affiliations

  1. Nonlinear Dynamics Group, Department of Electrical Engineering, Yeungnam University, 214-1 Dae-Dong, Kyongsan, 712-749, Republic of Korea

    Tae H. Lee, Ju H. Park & Zheng-Guang Wu

  2. National Laboratory of Industrial Control Technology, Institute of Cyber-Systems and Control, Zhejiang University, Yuquan Campus, Hangzhou Zhejiang, 310027, P.R. China

    Zheng-Guang Wu

  3. Division of IT Convergence/Division of Robotics System, DGIST, 50-1 Sang-Ri, Hyeonpung-Myeon, Dalseong-Gun, Daegu, 711-873, Republic of Korea

    Sang-Choel Lee & Dong Ha Lee

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  1. Tae H. Lee
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  2. Ju H. Park
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  3. Zheng-Guang Wu
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  4. Sang-Choel Lee
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  5. Dong Ha Lee
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Correspondence to Ju H. Park.

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Lee, T.H., Park, J.H., Wu, ZG. et al. Robust \(\mathcal{H}_{\infty}\) decentralized dynamic control for synchronization of a complex dynamical network with randomly occurring uncertainties. Nonlinear Dyn 70, 559–570 (2012). https://doi.org/10.1007/s11071-012-0477-0

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  • DOI: https://doi.org/10.1007/s11071-012-0477-0

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