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Uniform finite generation of the orthogonal group and applications to control theory
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Leite, Maria de Fátima da Silva (1982) Uniform finite generation of the orthogonal group and applications to control theory. PhD thesis, University of Warwick.

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Official URL: http://webcat.warwick.ac.uk/record=b3253627~S15
Abstract
A Lie group G is said to be uniformly finitely generated by one parameter subgroups exp (tX^1) , i = l,...,n , if there exists a positive integer k such that every element of G may be expressed as a product of at most k elements chosen alternatively from these oneparameter subgroups.
In this text we construct sets of left invariant vector fields on S0(n) , in particular pairs {A,B} , whose oneparameter subgroups uniformly finitely generate S0(n) . As a consequence, we also partially solve the uniform controllability problem for a m class of systems x(t) = ( m Σ i u1 (t)X1)x(t) , x ϵ S0(n) (X1,i = l,...,m)L A = so(n) by putting an upper bound on the number of switches in the trajectories, in positive time, of X1...,X m that are required to join any two points of S0(n) .
This result is also extended to any connected and paracompact 1/ C manifold of dimension n using a result of N. Levitt and H. Sussmann. An upper bound is put on the minimum number of switches of trajectories, in positive time, required to join any two states on M by two vector fields on M. This bound depends only on the dimension of M.
Item Type:  Thesis (PhD)  

Subjects:  Q Science > QA Mathematics  
Library of Congress Subject Headings (LCSH):  Control theory, Lie groups, Vector fields, Manifolds (Mathematics)  
Official Date:  1982  
Dates: 


Institution:  University of Warwick  
Theses Department:  Control Theory Centre  
Thesis Type:  PhD  
Publication Status:  Unpublished  
Supervisor(s)/Advisor:  Crouch, P.  
Sponsors:  Fundaçăo Calouste Gulbenkian  
Extent:  vii, 141 leaves  
Language:  eng 
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