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Geometric homogeneity with applications to finite-time stability

DSpace at IIT Bombay

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Field Value
 
Title Geometric homogeneity with applications to finite-time stability
 
Creator BHAT, SP
BERNSTEIN, DS
 
Subject nonlinear-systems
vector field
stabilization
feedback
stabilizability
geometric homogeneity
homogeneous systems
stability
finite-time stability
lyapunov theory
 
Description This paper studies properties of homogeneous systems in a geometric, coordinate-free setting. A key contribution of this paper is a result relating regularity properties of a homogeneous function to its degree of homogeneity and the local behavior of the dilation near the origin. This result makes it possible to extend previous results on homogeneous systems to the geometric framework. As an application of our results, we consider finite-time stability of homogeneous systems. The main result that links homogeneity and finite-time stability is that a homogeneous system is finite-time stable if and only if it is asymptotically stable and has a negative degree of homogeneity. We also show that the assumption of homogeneity leads to stronger properties for finite-time stable systems.
 
Publisher SPRINGER LONDON LTD
 
Date 2011-08-30T07:04:26Z
2011-12-26T12:58:49Z
2011-12-27T05:49:23Z
2011-08-30T07:04:26Z
2011-12-26T12:58:49Z
2011-12-27T05:49:23Z
2005
 
Type Article
 
Identifier MATHEMATICS OF CONTROL SIGNALS AND SYSTEMS, 17(2), 101-127
0932-4194
http://dx.doi.org/10.1007/s00498-005-0151-x
http://dspace.library.iitb.ac.in/xmlui/handle/10054/12228
http://hdl.handle.net/10054/12228
 
Language en