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Controllability of fractional-order damped systems with time-varying delays in control

Author(s): Bin-bin He, Hua-cheng Zhou, Chun-hai Kou
Affiliation(s): College of Urban Railway Transportation, Shanghai University of Engineering Science, Shanghai 201620, China; more
Corresponding email(s): hebinbin45@126.com, hczhou@amss.ac.cn, kouchunhai@dhu.edu.cn
Key Words: Controllability, Fractional-order damped systems, Time-varying delays, Gramian matrix

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Bin-bin He, Hua-cheng Zhou, Chun-hai Kou. Controllability of fractional-order damped systems with time-varying delays in control[J]. Frontiers of Information Technology & Electronic Engineering,in press.https://doi.org/10.1631/FITEE.1900736

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author="Bin-bin He, Hua-cheng Zhou, Chun-hai Kou",
journal="Frontiers of Information Technology & Electronic Engineering",
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publisher="Zhejiang University Press & Springer",
doi="https://doi.org/10.1631/FITEE.1900736"
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%A Bin-bin He
%A Hua-cheng Zhou
%A Chun-hai Kou
%J Frontiers of Information Technology & Electronic Engineering
%P 844-855
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doi="https://doi.org/10.1631/FITEE.1900736"

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T1 - Controllability of fractional-order damped systems with time-varying delays in control
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PB - Zhejiang University Press & Springer
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doi="https://doi.org/10.1631/FITEE.1900736"

Abstract
Chinese Summary
Academic Network
Reviewer Comment

Abstract: In this study, we focus on the controllability of fractional-order damped systems in linear and nonlinear cases with multiple time-varying delays in control. For the linear system based on the Mittag-Leffler matrix function, we define a controllability gramian matrix, which is useful in judging whether the system is controllable or not. Furthermore, in two special cases, we present serval equivalent controllable conditions which are easy to verify. For the nonlinear system, under the controllability of its corresponding linear system, we obtain a sufficient condition on the nonlinear term to ensure that the system is controllable. Finally, two examples are given to illustrate the theory.

带有时变时滞的分数阶阻尼系统可控性研究

何彬彬¹，周华成²，寇春海³
¹上海工程技术大学城市轨道交通学院，中国上海市，201620
²中南大学数学与统计学院，中国长沙市，410075
³东华大学理学院，中国上海市，201620

摘要：本文研究线性与非线性分数阶阻尼系统的可控性。该系统具有多重时变时滞，且时滞位于控制函数中。对于线性系统，基于Mittag-Leffler函数，定义一个可控性Gramian矩阵，该矩阵对于判定线性系统是否可控具有重要作用。此外，对于两种特殊线性系统，给出易于判别的若干等价可控性条件。对于非线性系统，在相应线性系统可控前提下，给出充分条件确保系统可控性。最后，给出两个数值示例验证结论有效性。

关键词组：可控性；分数阶阻尼系统；时变时滞；Gramian矩阵

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带有时变时滞的分数阶阻尼系统可控性研究

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