A novel controllability analysis of impulsive fractional linear time invariant systems with state delay and distributed delays in control

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.