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. 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. Realizability of transfer matrices in the constrained Roesser model is discussed. 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.