Controllability Criteria for Linear Fractional Differential Systems with State Delay and Impulses

This paper is concerned with the controllability of linear fractional differential systems with delay in state and impulses. The factors of such systems including fractional derivative, impulses, and delay are taken into account synchronously. The expression of state response for such systems is derived, and the sufficient and necessary conditions ofcontrollability criteria are established. Both the proposed criteria and illustrative examples show that the controllabilityproperty of the linear systems is dependent neither on the order of fractional derivative, on delay nor on impulses