Finite-Frequency Model Order Reduction of Linear Systems via Parameterized Frequency-dependent Balanced Truncation
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.
Cite
@article{arxiv.1602.04408,
title = {Finite-Frequency Model Order Reduction of Linear Systems via Parameterized Frequency-dependent Balanced Truncation},
author = {Xin Du and Peter Benner},
journal= {arXiv preprint arXiv:1602.04408},
year = {2017}
}
Comments
Preparing the submission for IEEE Transactions on Automatic control