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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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 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.

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:	Date Event 1982 UNSPECIFIED
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Publication Status:	Unpublished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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