Open AccessMinimal realization and approximation of commensurate linear fractional-order systems via Loewner matrix method
Author(s) -
Lingjie Meng,
Yang Xu,
Umair Zulfiqar,
Xin Du
Publication year - 2021
Publication title -
mathematical biosciences and engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.451
H-Index - 45
eISSN - 1551-0018
pISSN - 1547-1063
DOI - 10.3934/mbe.2021058
Subject(s) - interpolation (computer graphics) , realization (probability) , mathematics , transfer function , fractional calculus , mathematical optimization , order (exchange) , matrix (chemical analysis) , algorithm , computer science , statistics , animation , materials science , computer graphics (images) , finance , electrical engineering , economics , composite material , engineering
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.