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Publication Status: | Unpublished | ||||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