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

• Published in: IEEE transactions on signal processing Vol. 58; no. 8; pp. 4447 - 4453
• Main Authors: Sumanasena, B, Dewasurendra, D A, Bauer, P H
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.08.2010; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: 3-D systems; Applied sciences; Asymptotic stability; Detection, estimation, filtering, equalization, prediction; Distributed filtering; Exact sciences and technology; Fornasini-Marchesini model; Givone-Roesser model; global asymptotic stability; grid sensor networks; Information processing; Information theory; Information, signal and communications theory; Linear systems; Miscellaneous; Multidimensional systems; Nonlinear dynamical systems; nonlinear systems; Sensor systems; Services and terminals of telecommunications; Signal and communications theory; Signal processing; Signal, noise; Stability analysis; State-space methods; Sufficient conditions; Systems, networks and services of telecommunications; Telecommunications; Telecommunications and information theory; Telemetry. Remote supervision. Telewarning. Remote control; Wireless sensor networks; Non stationary system; Necessary and sufficient condition; Wireless telecommunication; Non linear phenomenon; Implementation; Remote sensing; Asymptotic stability; Distributed processing; 3-D systems; grid sensor networks; Signal detection; Filtering; Distributed filtering; Givone-Roesser model; global asymptotic stability; Theoretical study; State space method; Distributed system; Non linear system; Fornasini-Marchesini model; nonlinear systems; Linear system; Simulation; Telecommunication system; Information processing; Signal processing; Wireless network; Non linear effect; Sensor array
• ISSN: 1053-587X; 1941-0476
• DOI: 10.1109/TSP.2010.2048706

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.