Controllability analysis of multiple fractional order integro-differential damping systems with impulsive interpretation

We study the controllability criteria for a class of fractional integro-differential damped systems with impulsive perturbations. The solution representation is derived for both linear and non-linear damped systems, and the introduced formulations were constructed by employing Laplace transformation with Mittag-Leffler matrix function. We present necessary and sufficient conditions for the indicated systems to be controllable in finite dimensional spaces. Here, controllability conditions are proposed by using Grammian matrix as a powerful tool. Two numerical examples are also given at end to demonstrate the obtained theory.