Partial stability and boundedness of general dynamical systems on metric spaces

We develop new results for partial stability of invariant sets and boundedness of motions for dynamical systems defined on metric space using stability preserving mappings. Our results are applicable to a much larger class of systems than existing results, including dynamical systems that cannot be...

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Bibliographic Details
Published in:Nonlinear analysis 2003-02, Vol.52 (4), p.1295-1316
Main Authors: Michel, A.N., Molchanov, A.P., Sun, Y.
Format: Article
Language:English
Subjects:
Asymptotic stability
Boundedness of motions
Comparison system
Discrete event system
Dynamical system
Exponential stability
Invariant set
Lyapunov function
Partial stability
Stability
Stability preserving mapping
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Summary:We develop new results for partial stability of invariant sets and boundedness of motions for dynamical systems defined on metric space using stability preserving mappings. Our results are applicable to a much larger class of systems than existing results, including dynamical systems that cannot be determined by the usual classical (differential) equations and inequalities. In contrast to existing results which pertain primarily to the analysis of equilibria, present results apply to invariant sets (including equilibria as a special case). We apply our results in the analysis of a class of discrete event systems (a computer load balancing problem). We are not aware of existing results on partial stability that apply to this class of systems.
ISSN:0362-546X
1873-5215
DOI:10.1016/S0362-546X(02)00167-0