Controllability and observability of impulsive fractional linear time-invariant system

In this paper, we deal with the controllability and observability of impulsive fractional linear time-invariant (IF-LTI for short) system. Our main purpose is to built some necessary and sufficient conditions of controllability and observability for the IF-LTI system. At the same time, we establish some conclusions of controllability and observability for a continuous fractional LTI system, which is a special case of the IF-LTI system. Examples are given to illustrate our results.