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Title: On controllability and stability of uncertain systems
Author: Botelho, Marcus Antonio
ISNI:       0000 0001 3471 582X
Awarding Body: University of Warwick
Current Institution: University of Warwick
Date of Award: 1994
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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.
Supervisor: Not available Sponsor: Conselho Nacional De Desenvolvimento Cientifico e Tecnologico (CNPq-Brazil)
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available
Keywords: QA Mathematics