This paper proposes new state-space formulations of IIR Variable Digital Filters (VDFs) based on frequency transformations. The existing frequency transformation-based state-space VDFs require restrictions on the transfer functions, state-space representations, and tuning characteristics. On the other hand, the proposed method is free from such restrictions. We achieve this goal by applying series approximations to the conventional state-space formulations of frequency transformations. This approach also allows us to realize the proposed VDFs without complicated computations such as the inverse matrix and the square root. Furthermore, the proposed VDFs show high accuracy with respect to the finite wordlength effects as well as the approximation errors.