Controllability for a Class of Linear Time-Varying Impulsive Systems With Time Delay in Control Input

In this note, the controllability for a class of linear time varying impulsive systems with time delay in control input is studied. Sufficient and necessary conditions for the controllability of such systems are established. Specializing the obtained results to the cases of linear time-varying impulsive systems and linear time invariant impulsive systems with time delay, some simple criteria with respect to coefficient matrices, which are less conservative than some existing results are derived. It is also shown that the time delay in control input contributes to achieve the controllability of impulsive system even if the system is not controllable. Two examples are worked out to illustrate our results.