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Zbl 1142.93034
Liu, Shu-Jun; Zhang, Ji-Feng; Jiang, Zhong-Ping
A notion of stochastic input-to-state stability and its application to stability of cascaded stochastic nonlinear systems. (English)
[J] Acta Math. Appl. Sin., Engl. Ser. 24, No. 1, 141-156 (2008). ISSN 0168-9673; ISSN 1618-3932/e

Summary: 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.

MSC 2000:: *93E15 Stochastic stability
93C10 Nonlinear control systems
93E03 General theory of stochastic systems
93D25 Input-output approaches to stability of control systems

Keywords: stochastic nonlinear systems; stochastic input-to-state stability (SISS); SISS-Lyapunov function

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