Stability of Distributed 3-D Systems Implemented on Grid Sensor Networks

Using the Givone-Roesser and the Fornasini-Marchesini state space models for m-D systems, a method for distributed information processing in rectangular grid based wireless sensor networks is presented. It can be used for distributed implementation of any general linear system on a grid sensor network. Nonlinearities caused by finite precision number representation schemes used for in node computations and inter node communication are modeled. Stability of the system is analyzed with special consideration given to the influence of inter-node communication on system dynamics. A necessary and sufficient condition for global asymptotic stability under finite precision arithmetic is established. Simulation results are presented to illustrate the theoretical results.