The class of linear distributed dynamic systems is considered with the time variable that runs through the set of nonnegative integer numbers and the "spatial" variable that varies in a finite commutative group. The coefficients of systems belong to an arbitrary commutative ring with an identity. A criterion for controllability is obtained, and an algorithm for calculating the input actions that determine the transition to a given state is presented. It is shown that the controllability makes it possible to stabilize the system; i.e., there is a feedback such that all solutions are equal to zero beginning with a certain time instant. When the operator that specifies the system is invertible, it is established that the controllability is necessary for the system to be stabilized.
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