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ISSN:2164-6376 (print)
ISSN:2164-6414 (online)
Discontinuity, Nonlinearity, and Complexity

Dimitry Volchenkov (editor), Dumitru Baleanu (editor)

Dimitry Volchenkov(editor)

Mathematics & Statistics, Texas Tech University, 1108 Memorial Circle, Lubbock, TX 79409, USA

Email: dr.volchenkov@gmail.com

Dumitru Baleanu (editor)

Cankaya University, Ankara, Turkey; Institute of Space Sciences, Magurele-Bucharest, Romania

Email: dumitru.baleanu@gmail.com

A Novel Controllability Analysis of Impulsive Fractional Linear Time Invariant Systems with State Delay and Distributed Delays in Control

Discontinuity, Nonlinearity, and Complexity 7(3) (2018) 275--290 | DOI:10.5890/DNC.2018.09.006

Vadivoo B. Sundara$^{1}$, R. Raja$^{2}$, R. P. Agarwal$^{3}$, G. Rajchakit$^{4}$

$^{1}$ Department of Mathematics, Alagappa University, Karaikudi 630 004, India

$^{2}$ Ramanujan Centre For Higher Mathematics, Alagappa University, Karaikudi 630004, India

$^{3}$ Department of Mathematics, Texas A& M University-Kingsville, Kingsville 78363, USA

$^{4}$ Department of Mathematics, Faculty of Science, Maejo University, Chiang Mai, Thailand

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Abstract

In this paper, we investigate the controllability of impulsive fractional linear time invariant systems with state delay and distributed delays in control. By using the controllability Grammian matrix which is defined by the Mittag-Leffler matrix function , a new set of ufficient conditions are obtained for the considered system to be controllable. Finally, two numerical examples are given to demonstrate the validity of the obtained theoretical results.

Acknowledgments

This work was jointly supported by the Thailand research grant fund (RSA5980019) and Maejo University.

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