Minimal realization and approximation of commensurate linear fractional-order systems via Loewner matrix method

Abstract

In this paper we propose a data driven realization and model order reduction (MOR) for linear fractional-order system (FoS) by applying the Loewner-matrix method. Given the interpolation data which obtained by sampling the transfer function of a FoS, the minimal fractional-order state space descriptor model that matching the interpolation data is constructed with low computational cost. Based on the framework, the commensurate order α of the fractional-order system is estimated by solving a least squares optimization in terms of sample data in case of unknown order-α. In addition, we present an integer-order approximation model using the interpolation method in the Loewner framework for FoS with delay. Finally, several numerical examples demonstrate the validity of our approach.

Keywords

• data driven model reduction
• fractional-order system
• loewner framework
• interpolation
• time delay
• commensurate order