The paper concerns the representation of continuous-variable discrete-time systems with quantised input and state. It shows that the autonomous quantised system is represented by the Frobenius-Perron operator and the non-autonomous by the Foias operator. A finite and complete approximation of the Frobenius-Perron operator is given by an automaton which turns out to be identical to the discrete abstraction of the quantised system that is currently studied in the literature on verification or diagnosis of hybrid systems. Hence, the paper shows a connection between the mathematical literature and hybrid systems research. As a result of this connection it is shown that the abstraction converges to the continuous system for finer quantisation. The paper ends with presenting a method for the computation of abstractions that guarantees the completeness of the resulting model.