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CLC number: O231

On-line Access: 2021-02-01

Received: 2019-09-19

Revision Accepted: 2020-06-15

Crosschecked: 2020-08-19

Cited: 0

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Citations:  Bibtex RefMan EndNote GB/T7714


Jun-e Feng


Qing-le Zhang


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Frontiers of Information Technology & Electronic Engineering  2021 Vol.22 No.2 P.210-221


Solution and stability of continuous-time cross-dimensional linear systems

Author(s):  Qing-le Zhang, Biao Wang, Jun-e Feng

Affiliation(s):  School of Mathematics, Shandong University, Jinan 250100, China

Corresponding email(s):   zqlcfc03@163.com, wangbiao9956@163.com, fengjune@sdu.edu.cn

Key Words:  Cross-dimensional, V-addition, V-product, Asymptotic stability, Stabilization

Qing-le Zhang, Biao Wang, Jun-e Feng. Solution and stability of continuous-time cross-dimensional linear systems[J]. Frontiers of Information Technology & Electronic Engineering, 2021, 22(2): 210-221.

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author="Qing-le Zhang, Biao Wang, Jun-e Feng",
journal="Frontiers of Information Technology & Electronic Engineering",
publisher="Zhejiang University Press & Springer",

%0 Journal Article
%T Solution and stability of continuous-time cross-dimensional linear systems
%A Qing-le Zhang
%A Biao Wang
%A Jun-e Feng
%J Frontiers of Information Technology & Electronic Engineering
%V 22
%N 2
%P 210-221
%@ 2095-9184
%D 2021
%I Zhejiang University Press & Springer
%DOI 10.1631/FITEE.1900504

T1 - Solution and stability of continuous-time cross-dimensional linear systems
A1 - Qing-le Zhang
A1 - Biao Wang
A1 - Jun-e Feng
J0 - Frontiers of Information Technology & Electronic Engineering
VL - 22
IS - 2
SP - 210
EP - 221
%@ 2095-9184
Y1 - 2021
PB - Zhejiang University Press & Springer
ER -
DOI - 10.1631/FITEE.1900504

We investigate the solution and stability of continuous-time cross-dimensional linear systems (CCDLSs) with dimension bounded by v-addition and v-product. Using the integral iteration method, the solution to CCDLSs can be obtained. Based on the new algebraic expression of the solution and the Jordan decomposition method of matrix, a necessary and sufficient condition is derived for judging whether a CCDLS is asymptotically stable with a given initial state. This condition demonstrates a method for finding the domain of attraction and its relationships. Then, all the initial states that can be stabilized are studied, and a method for designing the corresponding controller is proposed. Two examples are presented to illustrate the validity of the theoretical results.





Darkslateblue:Affiliate; Royal Blue:Author; Turquoise:Article


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