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A notion of stochastic input-to-state stability and its application to stability of cascaded stochastic nonlinear systems

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Abstract

In this paper, the property of practical input-to-state stability and its application to stability of cascaded nonlinear systems are investigated in the stochastic framework. Firstly, the notion of (practical) stochastic input-to-state stability with respect to a stochastic input is introduced, and then by the method of changing supply functions, (a) an (practical) SISS-Lyapunov function for the overall system is obtained from the corresponding Lyapunov functions for cascaded (practical) SISS subsystems.

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Authors and Affiliations

  1. Department of Mathematics, Southeast University, Nanjing, 210096, China

    Shu-jun Liu

  2. Key Laboratory of Systems and Control, Institute of Systems Science, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100080, China

    Ji-feng Zhang

  3. Department of Electrical and Computer Engineering, Polytechnic University, 5 Metrotech Center, Brooklyn, N.Y., 11201, USA

    Zhong-ping Jiang

Authors
  1. Shu-jun Liu
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  2. Ji-feng Zhang
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  3. Zhong-ping Jiang
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Correspondence to Shu-jun Liu.

Additional information

Supported by the National Natural Science Foundation of China (No.60221301, No.60428304).

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Liu, Sj., Zhang, Jf. & Jiang, Zp. A notion of stochastic input-to-state stability and its application to stability of cascaded stochastic nonlinear systems. Acta Math. Appl. Sin. Engl. Ser. 24, 141–156 (2008). https://doi.org/10.1007/s10255-007-7005-x

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  • DOI: https://doi.org/10.1007/s10255-007-7005-x

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