Full Text:
<6306>
Summary: 
<1500>
CLC number: O231
On-line Access: 2024-08-27
Received: 2023-10-17
Revision Accepted: 2024-05-08
Crosschecked: 2020-04-30
Cited: 0
Clicked: 5027
Citations: Bibtex RefMan EndNote GB/T7714
https://orcid.org/0000-0002-8860-6263
Controllability of fractional-order damped systems with time-varying delays in control
| ||||||||||||||
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.
@article{title="Controllability of fractional-order damped systems with time-varying delays in control",
author="Bin-bin He, Hua-cheng Zhou, Chun-hai Kou",
journal="Frontiers of Information Technology & Electronic Engineering",
volume="21",
number="6",
pages="844-855",
year="2020",
publisher="Zhejiang University Press & Springer",
doi="10.1631/FITEE.1900736"
}
%0 Journal Article
%T Controllability of fractional-order damped systems with time-varying delays in control
%A Bin-bin He
%A Hua-cheng Zhou
%A Chun-hai Kou
%J Frontiers of Information Technology & Electronic Engineering
%V 21
%N 6
%P 844-855
%@ 2095-9184
%D 2020
%I Zhejiang University Press & Springer
%DOI 10.1631/FITEE.1900736
TY - JOUR
T1 - Controllability of fractional-order damped systems with time-varying delays in control
A1 - Bin-bin He
A1 - Hua-cheng Zhou
A1 - Chun-hai Kou
J0 - Frontiers of Information Technology & Electronic Engineering
VL - 21
IS - 6
SP - 844
EP - 855
%@ 2095-9184
Y1 - 2020
PB - Zhejiang University Press & Springer
ER -
DOI - 10.1631/FITEE.1900736
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.
[1]Balachandran K, Park JY, 2009. Controllability of fractional integrodifferential systems in Banach spaces. Nonl Anal Hybr Syst, 3(4):363-367.
[2]Balachandran K, Zhou Y, Kokila J, 2012a. Relative controllability of fractional dynamical systems with delays in control. Commun Nonl Sci Numer Simul, 17(9):3508-3520.
[3]Balachandran K, Kokila J, Trujillo JJ, 2012b. Relative controllability of fractional dynamical systems with multiple delays in control. Comput Math Appl, 64(10):3037-3045.
[4]Balachandran K, Govindaraj V, Rivero M, et al., 2015. Controllability of fractional damped dynamical systems. Appl Math Comput, 257:66-73.
[5]Dauer JP, 1976. Nonlinear perturbations of quasi-linear control systems. J Math Anal Appl, 54(3):717-725.
[6]Ge FD, Zhou HC, Kou CH, 2016. Approximate controllability of semilinear evolution equations of fractional order with nonlocal and impulsive conditions via an approximating technique. Appl Math Comput, 275:107-120.
[7]Gu KQ, Kharitonov VL, Chen J, 2003. Stability of Time-Delay Systems. Birkhäuser-Verlag, Boston, USA.
[8]He BB, Zhou HC, Kou CH, 2016a. The controllability of fractional damped dynamical systems with control delay. Commun Nonl Sci Numer Simul, 32:190-198.
[9]He BB, Zhou HC, Kou CH, 2016b. On the controllability of fractional damped dynamical systems with distributed delays. Proc 35th Chinese Control Conf, p.10418-10423.
[10]Hilfer R, 2000. Applications of Fractional Calculus in Physics. World Scientific Publisher, Singapore.
[11]Kilbas AA, Srivastava HM, Trujillo JJ, 2006. Theory and Applications of Fractional Differential Equations. Elsevier, Amsterdam, the Netherlands.
[12]Liu S, Yang R, Zhou XF, et al., 2019. Stability analysis of fractional delayed equations and its applications on consensus of multi-agent systems. Commun Nonl Sci Numer Simul, 73:351-362.
[13]Miller KS, Ross B, 1993. An Introduction to the Fractional Calculus and Fractional Differential Equation. Wiley-Interscience Publication, New York, USA.
[14]Monje CA, Chen Y, Vinagre BM, et al., 2010. Fractional-Order Systems and Controls: Fundamentals and Applications. Springer-Verlag, London, UK.
[15]Podlubny I, 1998. Fractional Differential Equations. Academic Press, New York, USA.
[16]Sikora B, Klamka J, 2017. Constrained controllability of fractional linear systems with delays in control. Syst Contr Lett, 106:9-15.
[17]Zhou Y, 2014. Basic Theory of Fractional Differential Equations. World Scientific Publisher, Singapore.
ORCID: 
Open peer comments: Debate/Discuss/Question/Opinion
<1>