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Realization using the FM model for implementations in distributed grid sensor networks

Based on the Fornasini-Marchesini and Roesser local state space models, a method for distributed information processing in grid sensor networks is presented in [1], [4]. The method can be employed to implement linear systems in grid sensor networks. For a system described by either state space model to be implementable in real-time on a sensor network, when information originating in a node cannot be conveyed over the entire sensor network in a single time slot, the system matrices of the state space model have to satisfy particular conditions. This constraint limits the type of systems implementable, in real-time on sensor networks, using the method proposed in [1], [4]. Realizability of transfer matrices in the constrained Roesser model is discussed in [5]. The analogous problem for FM model based implementations is addressed in this paper. A necessary and sufficient condition for a proper transfer matrix to be realizable in the constrained FM model is established. A realization algorithm to derive a FM model that satisfies the desired condition, given an admissible transfer matrix is also derived in this paper. The analogues problem for the realization of non-proper transfer matrices is also addressed.