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Abstract

The present thesis deals with some significant algebraic computations of Control Theory. The main problem examined in the Thesis concerns the properties of the Greatest Common Divisor (GCD) of a set of polynomials; these properties may be investigated using the Sylvester Resultant. New properties of the Sylvester Resultant linked to GCD are established and these lead to canonical factorisations of resultants expressing the extraction of common divisors from the elements of the original set. These results lead to a new representation of the GCD in terms of a canonical factorisation of the Sylvester Resultant obtained by a reduced Sylvester Resultant and a Toeplitz matrix representing the GCD.

The Sylvester resultant factorisation establishes the framework for the characterisation of the “approximate” GCD. The evaluation of the “optimal” approximate GCD and its “strength” comes as a result of the above framework. The problem of approximate factorisation of polynomials, a problem related to root clustering, is also considered and solved using the new techniques. The approximate GCD framework is applied to the case of Linear System properties and metrics measuring distances from fundamental properties are introduced.

Finally, an additional contribution consists of a detailed account of the parameterisation of the family of proper controllers as a solution of a scalar polynomial Diophantine equation.

Publication Type:	Thesis (Doctoral)
Subjects:	Q Science > QA Mathematics > QA75 Electronic computers. Computer science
Departments:	School of Science & Technology > Mathematics School of Science & Technology > School of Science & Technology Doctoral Theses Doctoral Theses

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