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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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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 one-parameter subgroups. In this text we construct sets of left invariant vector fields on S0(n) , in particular pairs {A,B} , whose one-parameter 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:  DOI: Not available
Keywords: QA Mathematics