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Boundedness of orbits and stability of closed sets

DSpace at IIT Bombay

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Field Value
 
Title Boundedness of orbits and stability of closed sets
 
Creator BHAT, SP
 
Subject systems
stability of sets
lyapunov stability
attractivity
boundedness
prolongations
nontangency
 
Description This paper explores fundamental connections between boundedness of orbits, and stability and attractivity of closed sets. For this purpose, the paper considers topological notions of stability and attractivity which do not depend on a metric. The notions considered are characterized in terms of restricted prolongations and positive limit sets, and connections with boundedness are studied. Finally, the notion of nontangency is used to give a Lyapunov result for Lyapunov stability, attractivity and boundedness of orbits. Unlike previous sufficient conditions for boundedness. our result does not require the Lyapunov function to be proper or weakly proper. Examples are provided to illustrate the results. (C) 2009
 
Publisher PERGAMON-ELSEVIER SCIENCE LTD
 
Date 2011-08-23T17:14:23Z
2011-12-26T12:56:32Z
2011-12-27T05:45:23Z
2011-08-23T17:14:23Z
2011-12-26T12:56:32Z
2011-12-27T05:45:23Z
2009
 
Type Article
 
Identifier NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 71(11), 5332-5343
0362-546X
http://dx.doi.org/10.1016/j.na.2009.04.038
http://dspace.library.iitb.ac.in/xmlui/handle/10054/10587
http://hdl.handle.net/10054/10587
 
Language en