This paper investigates, by using the state-space approach, some basic properties and state feedback compensation problem of n-dimensional discrete systems in the practical sense that the input and output signals of the systems are unbounded in, at most, one dimension. Notions of practical controllability, practical observability, practical stabilizability by state feedback and practical detectability are introduced and corresponding necessary and sufficient conditions are derived. Moreover, a connection between the state-space representation and doubly coprime matrix fractional description on the ring of practically stable rational functions is shown. The obtained results clarify that all the n-dimensional problems considered in the practical sense are in fact equivalent to the corresponding problems of n one-dimensional systems, hence can be essentially solved by using one-dimensional methods.