An input-output representation for implicit linear time-varying systems

The need to describe the input-output behavior of implicit differential systems arises in many contexts, including computer-aided modeling and the analysis of dynamical control systems. For a linear time-varying singular control system with real analytic coefficients in state space form, we produce an external (input-output) description of the system behavior in the form of a set of higher order differential equations in the inputs and outputs. The component of the state vector that affects the input-output relation is identified by a projection matrix which is computable from the original system coefficient matrices. The resulting input-output equations involve redundancy, but the input-output representation is obtained using computations on the original system without applying coordinate transformations.