Necessary and Sufficient Conditions for Controllability of Switched Impulsive Control Systems With Time Delay

This paper first introduces both impulsive and time-delay behavior into switched linear systems at the same time and studies the controllability and reachability of such systems. Necessary and sufficient criteria for reachability and controllability are established. It is proved that reachability is equivalent to controllability for such systems. Our criteria are of geometric type, they can be transformed into algebraic form conveniently. Finally, a numerical example is given to illustrate the utility of our criteria