A finite dimensional parameterization of linear time varying systems

In this paper we obtain a finite dimensional parameterization of linear time varying systems in discrete time. Subsequently we study the question of realization and analyze the stability properties of these systems. Our interest in the above finite dimensional parameterization problem stems from an interest to develop a robust stabilization theory via an adaptive control. The finite dimensionality of the space enables us to describe and analyze a structured family of time varying systems. In this paper, this program is initiated.