Finite-Frequency Model Order Reduction of Linear Systems via Parameterized Frequency-dependent Balanced Truncation
For control engineers needing reduced-order models accurate over specific frequency ranges, this method offers a theoretical error bound, though it is an incremental extension of existing balanced truncation techniques.
The paper proposes a parameterized frequency-dependent balanced truncation method for finite-frequency model order reduction of linear continuous-time systems, providing a finite-frequency error bound. Examples illustrate the approach.
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.