This paper presents a contribution to the study of the stability, stabiliza
bility, observers and compensators for discrete-time distributed systems wi
th delays in the state, the control and the output. Necessary and sufficien
t conditions for the stability are established. Stabilizability via feedbac
k control is considered. The observers and compensators for these systems a
re also considered. Sufficient conditions for their existence and methods f
or their construction are presented. To illustrate this work, some examples
are given.