Generalized state-space realizations from matrix fraction descriptions

The problem of the realization of a matrix fraction description (MFD) of a nonproper transfer function is considered. An algorithm for the realization is developed, and it is shown that it is a natural generalization of Wolovich's method (1973) for the case of proper systems. The resulting generalized state-space system is shown to be reachable, and the conditions for its minimality, in terms of the coprimeness and column reducedness of the MFD, are derived. The relation between the controllability indexes of the realization and the Forney order (1975) of the MFD is established.<
>