Finite-Frequency Model Order Reduction of Linear Systems via Parameterized Frequency-dependent Balanced Truncation

TL;DR

This paper introduces a novel finite-frequency model order reduction method for linear systems using parameterized frequency-dependent balanced truncation, providing finite-frequency error bounds and improved approximation within specified frequency ranges.

Contribution

The paper develops a new PFDBT method that incorporates PFD mappings to achieve finite-frequency model reduction with guaranteed error bounds, advancing balanced truncation techniques.

Findings

The PFDBT method effectively reduces model order within specified frequency ranges.

The approach provides finite-frequency error bounds for the reduced models.

Examples demonstrate the method's accuracy and applicability.

Abstract

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.