Output regulation problems are a class of problems that has high importance in systems control engineering. The solutions of such problems generally involve the design of an internal model based controller with error feedback structure that can also provide stability to the closed-loop system. Most of previous studies of such problems, however, are based on dynamical systems described by di erential equations for continuous-time and by di erence equations for discrete-time on the space of Rn. Few results have been obtained for dynamical systems with more abstract descriptions on sets with more general topologies. In this thesis, we use a set-theoretic approach with commutative diagrams to describe a dynamical system and its properties. Output regulation problems will also be de ned based on such dynamical systems. We will present su cient conditions for output regulation problems on complete metric spaces and Banach spaces.

Output regulation problems are a class of problems that has high importance in systems control engineering. The solutions of such problems generally involve the design of an internal model based controller with error feedback structure that can also provide stability to the closed-loop system. Most of previous studies of such problems, however, are based on dynamical systems described by di erential equations for continuous-time and by di erence equations for discrete-time on the space of Rn. Few results have been obtained for dynamical systems with more abstract descriptions on sets with more general topologies. In this thesis, we use a set-theoretic approach with commutative diagrams to describe a dynamical system and its properties. Output regulation problems will also be de ned based on such dynamical systems. We will present su cient conditions for output regulation problems on complete metric spaces and Banach spaces.

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The present work is divided in two parts. The first is concerned with the dynamics on the Grassmann manifold of k-dimensional subvector spaces of an n dimensional real or complex vector space induced by a linear invertible transformation A of the vector space into itself. The Grassmann map GA sends p to Ap, and one asks, what are the dynamics of GA? In the second part, I consider dynamics induced by a linear cocycle covering a diffeomorphism of a compact manifold, acting on the Grassmann bundle of k-dimensional linear subspaces of TN. I prove a Kupka-Smale theorem for the space of cocycles covering diffeomorphisms of a compact manifold. The proof of this theorem implies the same type of results for derived cocycles parametrized in the space of diffeomorphisms. The results of the second part can be generalized without effort to cocycles covering endomorphisms of N.

Thesis (Ph.D.)--Tufts University, 2004. / Adviser: Boris Hasselblatt. Submitted to the Dept. of Mathematics. Includes bibliographical references (leaves 61-62). Access restricted to members of the Tufts University community. Also available via the World Wide Web;

Thesis (Ph.D.)--University of Nebraska-Lincoln, 2007. / Title from title screen (site viewed May 20, 2008). PDF text: 77 p. ; 328 K. UMI publication number: AAT 3284240. Includes bibliographical references. Also available in microfilm and microfiche formats.

Thesis (Master)--İzmir Institute of Technology, İzmir, 2004. / Includes bibliographical references (leaves.55-57).

Thesis (Ph. D.)--Lehigh University, 2006. / Includes vita. Includes bibliographical references (leaves 72-76).