Botelho, Marcus Antonio (1994) On controllability and stability of uncertain systems. PhD thesis, University of Warwick.

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Abstract

In the first part of the work, we consider the problem of giving upper
bounds for Ix(T) - z(T)I, the error between the final states of a nominal finite dimensional system x = Ax + Bu, x(O) = Xo, and of the system disturbed by multiple structured perturbations of the form
r
z(t) = Az(t) + LDkFk(CkZ(t), t) + Bu(t)
k=l
which accounts for the uncertainties on the entries of the matrix A.
In approaching the problem we introduce a framework which involves
some weight-functions and provides a scaling technique that allows for
enlarging the class of perturbations and for getting lower bounds for
the error.
In the second part, we contribute towards the problem of robustness
of stability of i: = Ax. To account for the uncertainties we consider
linear but time-varying structured perturbations yielding the disturbed
system
z(O) = x;
i: = Ax + BD(t)Cx x(O) = Xo
We determine the real time-varying stability radius
rR,t = {IIDIILoo j the equilibrium of (*) is not asymptotically stable}
for the linear oscillator by means of a special algorithm. Also we study
its asymptotic behaviour for small dampings by using an averaging
method. Finally we study n-dimensional systems under periodic perturbations
and give a result which generalises the characterisation of
destabilising perturbation from time-invariant to that of time-varying
periodic perturbations.

Item Type:	Thesis (PhD)
Subjects:	Q Science > QA Mathematics
Library of Congress Subject Headings (LCSH):	Mathematics
Official Date:	June 1994
Dates:	Date Event June 1994 Created
Institution:	University of Warwick
Theses Department:	Mathematics Institute
Thesis Type:	PhD
Publication Status:	Unpublished
Supervisor(s)/Advisor:	Pritchard, A. J.
Sponsors:	Conselho Nacional De Desenvolvimento Cientifico e Tecnologico (CNPq-Brazil)
Language:	eng

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