The paper considers asymptotically stable periodic difference inclusions. The uniform character of the convergence of solutions to zero is established. For selector-linear difference inclusions the equivalence of the uniform asymptotic stability and the uniform exponential stability is proved, and a necessary and sufficient condition for the uniform asymptotic stability in the form of a certain limit relation is obtained. Examples of systems leading to periodic difference 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 alternating current, control systems with amplitude-frequency modulation, systems used to solve problems associated with the study of large electric power systems in the presence of forced oscillations.