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L2–L∞ filtering for stochastic systems driven by Poisson processes and Wiener processes

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  • Song, Bo
  • Zhang, Ya
  • Park, Ju H.
  • Huang, Huan

Abstract

This paper investigates the L2–L∞ filtering problem for stochastic systems driven by Poisson processes and Wiener processes. Firstly, this paper presents an approach to transform the expectation of stochastic integral with respect to Poisson process into the expectation of Lebesgue integral by the martingale theory. Then, based on this, a filter is designed to guarantee that the filtering error system is mean-square asymptotically stable and its L2–L∞ performance satisfies a prescribed level. Finally, a simulation example is given to illustrate the effectiveness of the proposed filtering scheme.

Suggested Citation

  • Song, Bo & Zhang, Ya & Park, Ju H. & Huang, Huan, 2016. "L2–L∞ filtering for stochastic systems driven by Poisson processes and Wiener processes," Applied Mathematics and Computation, Elsevier, vol. 276(C), pages 407-416.
    • Handle: RePEc:eee:apmaco:v:276:y:2016:i:c:p:407-416
    DOI: 10.1016/j.amc.2015.12.026
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    References listed on IDEAS

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    1. Ken Sennewald & Klaus Wälde, 2006. "“Itô's Lemma” and the Bellman Equation for Poisson Processes: An Applied View," Journal of Economics, Springer, vol. 89(1), pages 1-36, October.
    2. Gene M. Grossman & Elhanan Helpman, 1991. "Quality Ladders in the Theory of Growth," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 58(1), pages 43-61.
    3. Klaus Wälde, 2005. "Endogenous Growth Cycles," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 46(3), pages 867-894, August.
    4. Aghion, Philippe & Howitt, Peter, 1992. "A Model of Growth through Creative Destruction," Econometrica, Econometric Society, vol. 60(2), pages 323-351, March.
    5. Steger, Thomas M., 2005. "Stochastic growth under Wiener and Poisson uncertainty," Economics Letters, Elsevier, vol. 86(3), pages 311-316, March.
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    Cited by:

    1. Zhang, Jie & Ma, Lifeng & Liu, Yurong & Lyu, Ming & Alsaadi, Fuad E. & Bo, Yuming, 2017. "H∞ and l2−l∞ finite-horizon filtering with randomly occurring gain variations and quantization effects," Applied Mathematics and Computation, Elsevier, vol. 298(C), pages 171-187.
    2. Li, Yueyang & Liu, Shuai & Zhong, Maiying & Ding, Steven X., 2018. "State estimation for stochastic discrete-time systems with multiplicative noises and unknown inputs over fading channels," Applied Mathematics and Computation, Elsevier, vol. 320(C), pages 116-130.

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