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H∞ analysis of nonlinear stochastic time-delay systems

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  • Shu, Huisheng
  • Wei, Guoliang

Abstract

In this paper, the H∞ analysis problem is studied for a general class of nonlinear stochastic systems with time-delay. The stochastic systems are described in terms of stochastic functional differential equations. The Razumikhin-type lemma is employed to establish sufficient conditions for the time-delay stochastic systems to be internally stable, and the H∞ analysis problem is studied in order to quantify the disturbance rejection attenuation level of the nonlinear stochastic time-delay system. In particular, the paper obtains the general conditions under which the L2 gain of the system is less than or equal to a given constant. Some easy-to-test criteria are also given so as to determine whether the nonlinear stochastic time-delay system under investigation is internally stable and whether it achieves certain H∞ performance index. Finally, illustrative examples are provided to show the usefulness of the proposed theory.

Suggested Citation

  • Shu, Huisheng & Wei, Guoliang, 2005. "H∞ analysis of nonlinear stochastic time-delay systems," Chaos, Solitons & Fractals, Elsevier, vol. 26(2), pages 637-647.
    • Handle: RePEc:eee:chsofr:v:26:y:2005:i:2:p:637-647
    DOI: 10.1016/j.chaos.2005.01.025
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    References listed on IDEAS

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    1. Mao, Xuerong, 1996. "Razumikhin-type theorems on exponential stability of stochastic functional differential equations," Stochastic Processes and their Applications, Elsevier, vol. 65(2), pages 233-250, December.
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    Cited by:

    1. Guoliang Wei & Zidong Wang & Wangyan Li & Lifeng Ma, 2014. "A Survey on Gain-Scheduled Control and Filtering for Parameter-Varying Systems," Discrete Dynamics in Nature and Society, Hindawi, vol. 2014, pages 1-10, April.
    2. Gao, Huijun & Lam, James & Wang, Zidong, 2007. "Discrete bilinear stochastic systems with time-varying delay: Stability analysis and control synthesis," Chaos, Solitons & Fractals, Elsevier, vol. 34(2), pages 394-404.
    3. Wei, Guoliang & Shu, Huisheng, 2007. "H∞ filtering on nonlinear stochastic systems with delay," Chaos, Solitons & Fractals, Elsevier, vol. 33(2), pages 663-670.
    4. Yue, Dong & Lam, James & Wang, Zidong, 2009. "Persistent disturbance rejection via state feedback for networked control systems," Chaos, Solitons & Fractals, Elsevier, vol. 40(1), pages 382-391.
    5. Wei, Guoliang & Wang, Zidong & Shu, Huisheng, 2008. "Nonlinear H∞ control of stochastic time-delay systems with Markovian switching," Chaos, Solitons & Fractals, Elsevier, vol. 35(3), pages 442-451.

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