Input-output structure of linear differential/algebraic systems

The problem of describing the input-output structure of general linear differential/algebraic systems is addressed. Explicit formulas are given in terms of the original parameters for systems with an arbitrary amount of redundancy. These formulas allow one to establish whether the system determines an input-output relation at all, and if so, they describe the rank of the transfer matrix and its pole/zero structure at infinity. The formulas may be seen as generalizations of a number of classical results on the input-output structure of standard state-space systems and descriptor systems, satisfying certain constraints. For the derivation, the pencil representation rather than the descriptor representation is used