Acta Mathematicae Applicatae Sinica, English Series

, Volume 24, Issue 1, pp 141–156

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

Article

DOI: 10.1007/s10255-007-7005-x

Cite this article as:
Liu, S., Zhang, J. & Jiang, Z. Acta Math. Appl. Sin. Engl. Ser. (2008) 24: 141. doi:10.1007/s10255-007-7005-x

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.

Keywords

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

2000 MR Subject Classification

93C1093E0393E15

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