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A notion of stochastic input-to-state stability and its application to stability of cascaded stochastic nonlinear systems. (English) Zbl 1142.93034
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:
93E15Stochastic stability
93C10Nonlinear control systems
93E03General theory of stochastic systems
93D25Input-output approaches to stability of control systems
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