This paper introduces a non-Euclidean parametrization of linear dynamical systems both in the open loop and in the closed loop. In particular, the various parametrizations introduced have a bundle structure which appears to be of relevance in system identification. Furthermore a quotient topology is obtained on the space of all systems and compared with the well-known graph topology. The article describes, many desirable features of the quotient topology. Applications of vector bundle and fiber bundle theory in parametrization of control systems in the closed loop introduced in this paper are new.