In this paper, we establish the controllability conditions for a finite-dimensional dynamical control system modelled by a linear impulsive matrix Lyapunov ordinary differential equations having multiple constant time-delays in control for certain classes of admissible control functions. We characterize the controllability property of the system in terms of matrix rank conditions and are easy to verify. The obtained results are applicable for both autonomous (time-invariant) and non-autonomous (time-variant) systems. Two numerical examples are given to illustrate the theoretical results obtained in this paper.
controllability, impulsive differential systems, matrix Lyapunov systems, delays
34A37, 93B05, 93C05, 93C15