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Abstract

The present thesis deals with the study of algebraic, geometric and feedback properties of singular systems. The theory that will be presented in this thesis falls within an area of research that is referred to as the "matrix pencil approach" to the geometric theory of linear systems. The two fundamental parts of this approach are the geometric theory of linear systems and the algebraic theory of matrix pencils. The work presented here is an attempt to unify the geometric, algebraic and dynamic aspects of linear system problems, which may be reduced to the study of properties of generalised autonomous differential systems y (F,G) : Fx=Gx, F,G e Rmxn. The general results, provide the means for investigating the properties of singular systems. The basic philosophy underlying the geometric approach to linear systems is that a system is an entity defined by a number of mappings defined on abstract linear spaces (the input, the state and the output space); several relevant structural features of the system are therefore determined by the way in which these mappings interact in their domains and codomains. These structural features can be expressed in terms of the geometrical properties of different types of subspaces connected with these mappings. Questions involving the existence and synthesis of controllers may be reduced to problems concerning the interrelationships of certain subspaces and the existence of mappings with given properties.

Publication Type:	Thesis (Doctoral)
Subjects:	Q Science > QA Mathematics
Departments:	School of Science & Technology > Mathematics School of Science & Technology > School of Science & Technology Doctoral Theses Doctoral Theses

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