First order representations of time-varying linear systems

We construct a special type of first order representation of a linear time-varying system given by linear ordinary differential equations with rational or meromorphic coefficients. Under certain conditions, such a representation yields a classical state space model. We show that every system admits a partition of its variables into inputs and outputs such that a state representation can be obtained. All the problems addressed in this paper can be solved algorithmically using non-commutative computer algebra over the polynomial ring K[s], where K is the field of rational or meromorphic functions, and we have the commutator rule sk - ks = k´ for k isin K, reflecting the product rule of differentiation