Stability preserving mappings for stochastic dynamical systems

We first formulate a general model for stochastic dynamical systems that is suitable in the stability analysis of invariant sets. This model is sufficiently general to include as special cases most of the stochastic systems considered in the literature. We then adapt several existing stability conce...

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Bibliographic Details
Published inIEEE transactions on automatic control Vol. 46; no. 6; pp. 933 - 938
Main Authors Ling Hou, Michel, A.N.
Format Journal Article
LanguageEnglish
Published New York IEEE 01.06.2001
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects
Clouds
Differential equations
Dynamical systems
Indium tin oxide
Large-scale systems
Lyapunov method
Mapping
Preserving
Stability
Stability analysis
Stochastic systems
Stochasticity
Theorems
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Summary:We first formulate a general model for stochastic dynamical systems that is suitable in the stability analysis of invariant sets. This model is sufficiently general to include as special cases most of the stochastic systems considered in the literature. We then adapt several existing stability concepts to this model and we introduce the notion of stability preserving mapping of stochastic dynamical systems. Next, we establish a result which ensures that a function is a stability preserving mapping, and we use this result in proving a comparison stability theorem for general stochastic dynamical systems. We apply the comparison stability theorem in the stability analysis of dynamical systems determined by Ito differential equations.
Bibliography:ObjectType-Article-2
SourceType-Scholarly Journals-1
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content type line 23
ISSN:0018-9286
1558-2523
DOI:10.1109/9.928598