An analysis on approximate controllability of semilinear control systems with impulsive effects

The article uses semigroup theory and Gronwall’s inequality to investigate the approximate controllability of impulsive semilinear control systems. A weaker Lipschitz condition on nonlinearity is enforced to reach the main conclusions. Two sets of assumptions have been used to discuss the key findings. As noted before by various researchers in the accessible literature, application of standard fixed point theorems such as Banach, Schauder, Sadovskii, and others is avoided. Finally, in order to verify the theoretical findings, one case study based on the presented topic is discussed.