ALGEBRAIC INTERPRETATION OF A LAPLACE TRA NSFORM AND TRANSFER-MATRICES

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 w here, even in the time-varying case, a (formal) Laplace transform and the transfer matrix are most naturally defined. Several classic proble ms are examined in this algebraic setting: the relationship between le ft (right) coprime matrix decomposition and controllability (observabi lity), the state-variable canonical realization, the transfer algebra with respect to parallel and series connections, the input-output inve rsion, and model matching.