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A realization problem of time-varying systems specified by a transfer matrix is also addressed. It is shown that realizability is equivalent to properness and minimality is equivalent to both controllability and observability. The notions of coprimeness of a matrix fraction description and row-properness of a skew polynomial matrix are introduced and used to determine the size of a minimal realization. An algorithm to transfer a given skew polynomial matrix into row-proper form is given and it is used to compute one sided greatest common divisors and least common multiples.","abstract_html":"The main goal of this thesis is to examine linear dynamical systems, both in the continuous- and discrete-time case, with time-varying coefficients using module theory and homological methods and to generalize results, such as the realization problem and matrix fraction descriptions, from the time-invariant case to the time-varying case. 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