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H∞ control for stochastic systems with Poisson jumps

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Abstract

This paper discusses the H ∞ control problem for a class of linear stochastic systems driven by both Brownian motion and Poisson jumps. The authors give the basic theory about stabilities for such systems, including internal stability and external stability, which enables to prove the bounded real lemma for the systems. By means of Riccati equations, infinite horizon linear stochastic state-feedback H ∞ control design is also extended to such systems.

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Authors and Affiliations

  1. School of Mathematics, Shandong University, Jinan, 250100, China

    Xiangyun Lin

  2. College of Science, Shandong University of Science and Technology, Qingdao, 266510, China

    Xiangyun Lin

  3. College of Information Science and Technology, Shandong University of Science and Technology, Qingdao, 266510, China

    Rui Zhang

Authors
  1. Xiangyun Lin
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  2. Rui Zhang
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Correspondence to Xiangyun Lin.

Additional information

This research is supported by the National Natural Science Foundation of China under Grant Nos. 60874032 and 70971079.

This paper was recommended for publication by Editor Guohua ZOU.

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Lin, X., Zhang, R. H∞ control for stochastic systems with Poisson jumps. J Syst Sci Complex 24, 683–700 (2011). https://doi.org/10.1007/s11424-011-9085-1

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  • DOI: https://doi.org/10.1007/s11424-011-9085-1

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