Use this URL to cite or link to this record in EThOS:  https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.345227 
Title:  Uniform finite generation of the orthogonal group and applications to control theory  
Author:  Leite, Maria de Fátima da Silva 
ISNI:
0000 0001 3411 0097


Awarding Body:  University of Warwick  
Current Institution:  University of Warwick  
Date of Award:  1982  
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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.


Supervisor:  Not available  Sponsor:  Fundaçăo Calouste Gulbenkian  
Qualification Name:  Thesis (Ph.D.)  Qualification Level:  Doctoral  
EThOS ID:  uk.bl.ethos.345227  DOI:  Not available  
Keywords:  QA Mathematics  
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