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Using the Givone-Roesser model for m-D systems, a method for distributed information processing in rectangular grid based sensor networks is presented. The method enables a distributed implementation of linear systems on a sensor network. Nonlinearities caused by quantization schemes used for in node computations and inter node communication are modeled. Global asymptotic stability of the system under quantization is analyzed. Special consideration is given to the effect of inter-node communication in system stability. Wireless sensor networks consisting of a large number of sensor nodes have emerged recently as a candidate for a wide variety of applications. Some of these applications require the sensor nodes to be placed in a regular grid.
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