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Decentralized Stabilization of Linear Systems via Limited Capacity Communication Networks

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2 Author(s)
Matveev, A.S. ; Department of Mathematics and Mechanics, Saint Petersburg University, Universitetskii 28, Petrodvoretz, St.Petersburg, 198504, Russia almat@am1540.spb.edu ; Savkin, A.V.

The paper addresses feedback stabilization of discrete-time linear systems with multiple sensors, controllers, and actuators. The information is transmitted between them via a limited capacity deterministic communication network with arbitrary topology, which may be dynamically changed by nodes authorized to switch channels. The transferred messages may be delayed, corrupted or even lost; they may interfere and collide with each other. It is shown that the criterion for stabilizability is given by the network rate region, which answers to the question: how much information can be reliably transmitted from one set of points to another set of points. The system is stabiliazible if and only if a certain vector characterizing its rate of instability in the open-loop lies in the interior of the rate domain. In general, the rate domain of the primal network is not relevant here and a certain extension of the network should be employed. Furthermore, the relevant rate domain corresponds to a special subclass of decoders. In some cases, all decoders can be considered and this domain equals the standard one.

Published in:

Decision and Control, 2005 and 2005 European Control Conference. CDC-ECC '05. 44th IEEE Conference on

Date of Conference:

12-15 Dec. 2005