The paper considers a periodic differential inclusion with an asymptotically stable set. The uniform character of convergence of solutions to an asymptotically stable set is established. An exponential estimate is obtained for solutions of a periodic differential inclusion homogeneous in state vector. Examples of control systems leading to consideration of periodic differential inclusions are given. These results can find applications in the stability analysis of control systems with periodic parameters, in particular, servomechanisms whose elements operate on AC, control systems with pulse amplitude modulation, and systems used to solve problems related to investigating vibrations of milling machines.