Approximate controllability for abstract measure differential systems

In this paper, we investigate approximate controllability for abstract measure differential systems based on generalizing knowledge for ordinary differential systems. We first introduce new concepts of the reachable set and approximate controllability for abstract measure differential systems. Then based on the nonlinear alternative for αα-condensing mapping in Banach space, we present sufficient conditions of approximate controllability for a class of abstract measure differential systems. Our results in dealing with approximate controllability are less conservative than those in the previous literature. Finally, an example is given to illustrate the availability of our results for approximate controllability.