Abstract: Two computationally efficient state-space structures for general 2-D digital systems described by Roesser s local state-space model are presented. Some properties of controllability and observability Gramians of the above two structures are derived. The overall roundoff noise model of 2-D digital systems implemented with fixed-point arithmetic is given. On the basis of the above theory, the low roundoff noise optimal state-space realizations of general 2-D digital systems are obtained. Finally, an example is given to demonstrate the differences of round- off noise arid computational efficiency between the above two structures.