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

  • Shu-jun Liu
  • Ji-feng Zhang
  • Zhong-ping Jiang


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.


Stochastic nonlinear systems Stochastic input-to-state stability (SISS) SISS-Lyapunov function 

2000 MR Subject Classification

93C10 93E03 93E15 


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Copyright information

© Springer-Verlag 2008

Authors and Affiliations

  1. 1.Department of MathematicsSoutheast UniversityNanjingChina
  2. 2.Key Laboratory of Systems and Control, Institute of Systems Science, Academy of Mathematics and Systems ScienceChinese Academy of SciencesBeijingChina
  3. 3.Department of Electrical and Computer EngineeringPolytechnic UniversityBrooklynUSA

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