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

Bin-bin HE; Hua-cheng ZHOU; Chun-hai KOU

doi:10.1631/FITEE.1900736

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

Special Feature on New Trends in Fractional Calculus for Information Science | Updated：2022-05-19

- Controllability of fractional-order damped systems with time-varying delays in control
- 带有时变时滞的分数阶阻尼系统可控性研究
- Frontiers of Information Technology & Electronic Engineering Vol. 21, Issue 6, Pages: 844-855(2020)
- Affiliations：
  
  College of Urban Railway Transportation, Shanghai University of Engineering Science, Shanghai 201620, China
  School of Mathematics and Statistics, Central South University, Changsha 410075, China
  Department of Applied Mathematics, Donghua University, Shanghai 201620, China
- Author bio：
  
  [ "Bin-bin HE, E-mail: hebinbin45@126.com" ]
  Hua-cheng ZHO, E-mail: hczhou@amss.ac.cn
  [ "Chun-hai KOU, E-mail: kouchunhai@dhu.edu.cn" ]
- Funds：
- DOI：10.1631/FITEE.1900736
  CLC： O231
- Received：28 December 2019，
  
  Revised：2020-;4-30，
  
  Published：2020-06
- Accepted：
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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, 2020, 21(6): 844-855.
DOI：

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, 2020, 21(6): 844-855. DOI： 10.1631/FITEE.1900736.

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。

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.

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Keywords

references

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