  Balanced truncation is one of the most common model order reduction schemes.
In this paper, we study finite-frequency model order reduction (FF-MOR)
problems of linear continuous-time systems within the framework of balanced
truncation method. Firstly, we construct a family of parameterized
frequency-dependent (PFD) mappings which generate discrete-time PFD mapped
systems and continuous-time PFD mapped systems of the given continuous-time
system. The relationships between the maximum singular value of the given
system over pre-specified frequency ranges and the maximum singular value of
the PFD mapped systems over entire frequency range are established. By
exploiting the properties of the discrete-time PFD mapped systems, a new
parameterized frequency-dependent balanced truncation (PFDBT) method providing
finite-frequency type error bound with respect to the maximum singular value of
the approximation error systems are developed. Examples are included for
illustration.
