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Robust Stabilization for Dynamic Systems with Multiple Time-Varying Delays and Nonlinear Uncertainties

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  • J. H. Park

    (Yeungnam University)

Abstract

In this paper, the problem of the robust stabilization for a class of uncertain linear systems with multiple time-varying delays is investigated. The uncertainty is nonlinear time-varying and does not require a matching condition. A memoryless state-feedback controller for the robust stabilization of the system is proposed. Based on the Lyapunov method and the linear matrix inequality (LMI) approach, two sufficient conditions for the stability are derived. Two numerical examples are given to illustrate the proposed method.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joptap:v:108:y:2001:i:1:d:10.1023_a:1026470106976
    DOI: 10.1023/A:1026470106976
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    Citations

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    Cited by:

    1. Park, Ju H., 2009. "Synchronization of cellular neural networks of neutral type via dynamic feedback controller," Chaos, Solitons & Fractals, Elsevier, vol. 42(3), pages 1299-1304.
    2. Chun Yin & Shouming Zhong & Xiaoyun Liu & Zijian Liu, 2011. "Novel Delay-Dependent Stabilization Criterion for Lur’e Systems with Sector-Restricted Nonlinearities and External Disturbances via PD Feedback Approach," Journal of Optimization Theory and Applications, Springer, vol. 151(1), pages 81-99, October.
    3. 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.
    4. O. M. Kwon & J. H. Park & S. M. Lee, 2008. "Exponential Stability for Uncertain Dynamic Systems with Time-Varying Delays: LMI Optimization Approach," Journal of Optimization Theory and Applications, Springer, vol. 137(3), pages 521-532, June.
    5. O. M. Kwon & J. H. Park, 2006. "Robust H ∞ Filtering for Uncertain Time-Delay Systems: Matrix Inequality Approach," Journal of Optimization Theory and Applications, Springer, vol. 129(2), pages 309-324, May.
    6. Shen, Chang-Chun & Zhong, Shou-Ming, 2009. "New delay-dependent robust stability criterion for uncertain neutral systems with time-varying delay and nonlinear uncertainties," Chaos, Solitons & Fractals, Elsevier, vol. 40(5), pages 2277-2285.
    7. Yan, Huaicheng & Huang, Xinhan & Wang, Min & Zhang, Hao, 2007. "Delay-dependent stability criteria for a class of networked control systems with multi-input and multi-output," Chaos, Solitons & Fractals, Elsevier, vol. 34(3), pages 997-1005.
    8. 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.
    9. O. M. Kwon & J. H. Park & S. M. Lee, 2010. "An Improved Delay-Dependent Criterion for Asymptotic Stability of Uncertain Dynamic Systems with Time-Varying Delays," Journal of Optimization Theory and Applications, Springer, vol. 145(2), pages 343-353, May.
    10. Park, Ju H. & Lee, S.M. & Kwon, O.M., 2009. "On exponential stability of bidirectional associative memory neural networks with time-varying delays," Chaos, Solitons & Fractals, Elsevier, vol. 39(3), pages 1083-1091.
    11. Yan, Huaicheng & Huang, Xinhan & Wang, Min & Zhang, Hao, 2008. "New delay-dependent stability criteria of uncertain linear systems with multiple time-varying state delays," Chaos, Solitons & Fractals, Elsevier, vol. 37(1), pages 157-165.
    12. Yuanqiang Chen & Honglei Xu, 2012. "Exponential stability analysis and impulsive tracking control of uncertain time-delayed systems," Journal of Global Optimization, Springer, vol. 52(2), pages 323-334, February.
    13. T. Senthilkumar & P. Balasubramaniam, 2011. "Delay-Dependent Robust Stabilization and H ∞ Control for Nonlinear Stochastic Systems with Markovian Jump Parameters and Interval Time-Varying Delays," Journal of Optimization Theory and Applications, Springer, vol. 151(1), pages 100-120, October.

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