Abstract
The tensor product of the module of a linear system with the quotient field of the ring of linear differential operators is a vector space where, even in the time-varying case, a (formal) Laplace transform and the transfer matrix are most naturally defined. Several classic problems are examined in this algebraic setting: the relationship between left (right) coprime matrix decomposition and controllability (observability), the state-variable canonical realization, the transfer algebra with respect to parallel and series connections, the input-output inversion, and model matching.
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