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A method for distributed information processing in grid sensor networks using the Fornasini-Marchesini (FM) local state space model has been proposed in the literature recently. The method can be used to implement linear systems in grid sensor networks. It can be shown that, the system matrices of the FM state space model have to satisfy particular conditions for the system to be implementable in real time in a sensor network. This constraint limits the type of systems implementable in real time on sensor networks. A necessary and sufficient condition for a causal transfer matrix to be realizable in the constrained FM model is established. A realization algorithm to derive an FM model that satisfies the desired condition, given an admissible causal transfer matrix, is also derived. The corresponding problem for the realization of noncausal transfer matrices is also addressed.