Discontinuity, Nonlinearity, and Complexity
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) 275290  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 UniversityKingsville, 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 MittagLeffler 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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