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

doi:10.1007/s10255-007-7005-x

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

Electrical and Computer Engineering

Research output: Contribution to journal › Article › peer-review

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.

Original language	English (US)
Pages (from-to)	141-156
Number of pages	16
Journal	Acta Mathematicae Applicatae Sinica
Volume	24
Issue number	1
DOIs	https://doi.org/10.1007/s10255-007-7005-x
State	Published - Jan 2008

Keywords

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

ASJC Scopus subject areas

Applied Mathematics

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10.1007/s10255-007-7005-x

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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.",

keywords = "SISS-Lyapunov function, Stochastic input-to-state stability (SISS), Stochastic nonlinear systems",

author = "Liu, {Shu Jun} and Zhang, {Ji Feng} and Jiang, {Zhong Ping}",

note = "Funding Information: Manuscript received January 8, 2007. Revised April 27, 2007. Supported by the National Natural Science Foundation of China (No.60221301,",

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AU - Liu, Shu Jun

AU - Zhang, Ji Feng

AU - Jiang, Zhong Ping

N1 - Funding Information: Manuscript received January 8, 2007. Revised April 27, 2007. Supported by the National Natural Science Foundation of China (No.60221301,

PY - 2008/1

Y1 - 2008/1

N2 - 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.

AB - 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.

KW - SISS-Lyapunov function

KW - Stochastic input-to-state stability (SISS)

KW - Stochastic nonlinear systems

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

Abstract

Keywords

ASJC Scopus subject areas

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