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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

Clicked: 4401

Citations:  Bibtex RefMan EndNote GB/T7714

 ORCID:

Jun-e Feng

https://orcid.org/0000-0003-3881-3042

Qing-le Zhang

https://orcid.org/0000-0002-4801-6672

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

http://doi.org/10.1631/FITEE.1900504


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",
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pages="210-221",
year="2021",
publisher="Zhejiang University Press & Springer",
doi="10.1631/FITEE.1900504"
}

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%T Solution and stability of continuous-time cross-dimensional linear systems
%A Qing-le Zhang
%A Biao Wang
%A Jun-e Feng
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%I Zhejiang University Press & Springer
%DOI 10.1631/FITEE.1900504

TY - JOUR
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
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SP - 210
EP - 221
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PB - Zhejiang University Press & Springer
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DOI - 10.1631/FITEE.1900504


Abstract: 
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.

跨维数线性连续系统的解和稳定性


张庆乐,王彪,冯俊娥
山东大学数学学院,中国济南市,250100

摘要:利用V-加法和V-乘法研究了维数有界的跨维数线性连续系统(CCDLSs)的解和稳定性。使用积分迭代法,得到CCDLSs的解。基于解的代数表示以及矩阵的若尔当分解,给出相应的充要条件判断一个CCDLS在给定初始状态后是否渐进稳定。该条件提供了一种确定吸引域以及吸引域间关系的方法。然后,研究了所有可镇定的初始状态,并提出相应控制器的设计方法。最后,给出两个例子说明理论结果的有效性。

关键词:跨维数;V-加法;V-乘法;渐进稳定性;镇定性

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

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