Abstract
In this work, we investigate the controllability of singular dynamic systems on time scales. First, we decompose the consider systems into a slow subsystem and a fast subsystem. After that, we use the Laplace transform and convolution theorem to derive the state response of these two subsystems. Finally, we established some necessary and sufficient conditions for the controllability of the slow subsystem and fast subsystem. At last, we provide an example to illustrate the obtained analytical results.