Open AccessBalanced truncation with ε‐embedding for coupled dynamical systems
Author(s) -
Jiang YaoLin,
Chen ChunYue,
Yang Ping
Publication year - 2018
Publication title -
iet circuits, devices and systems
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.251
H-Index - 49
eISSN - 1751-8598
pISSN - 1751-858X
DOI - 10.1049/iet-cds.2017.0349
Subject(s) - embedding , truncation (statistics) , truncation error , cholesky decomposition , stability (learning theory) , computer science , control theory (sociology) , order (exchange) , upper and lower bounds , mathematics , mathematical optimization , algorithm , mathematical analysis , physics , eigenvalues and eigenvectors , control (management) , quantum mechanics , machine learning , artificial intelligence , finance , economics
The authors focus on exploring the ε ‐embedding balanced truncation method of coupled systems. First, the coupled system is converted into a closed‐loop system. Then, the ε ‐embedding technique and the Cholesky factor‐alternating direction implicit algorithm are introduced to establish the balanced truncation method. The error bound and the stability of the resulting reduced‐order system are discussed. Furthermore, the proposed method is applied to reduce the order of each subsystem such that the original interconnected structure is preserved. The error bound and the stability of the corresponding reduced‐order system are also investigated. Finally, two numerical examples are employed to demonstrate the efficiency of the proposed method.