Conditions are investigated in this article for uniquely determining parameters of a descriptor system from time-domain noise-free input/output data, in which system matrices depend on its parameters through a linear fractional transformation. This model includes networked dynamic systems as its special cases. A bilinear matrix equality-based necessary and sufficient condition has been derived, which can be verified in principle for a low-dimensional system. Moreover, a computationally attractive condition is derived under the orthogonality of some transfer function matrices. These results completely remove the full-rank assumption required in the available studies. A circuit example is given to illustrate their properties.