Brief paper: Tradeoffs between quantization and packet loss in networked control of linear systems

Authors:
Koji Tsumura;Hideaki Ishii;Hiroto Hoshina
Affiliations:
Department of Information Physics and Computing, The University of Tokyo, 7-3-1, Hongo, Bunkyo-ku, Tokyo 113-8656, Japan;Department of Computational Intelligence and Systems Science, Tokyo Institute of Technology, 4259-J2-54, Nagatsuta-cho, Midori-ku, Yokohama 226-8502, Japan;Hitachi Global Storage Technologies Japan, Ltd., 1 Kirihara-cho, Fujisawa, Kanagawa 252-8588, Japan
Venue:
Automatica (Journal of IFAC)
Year:
2009

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Abstract

In this paper, we consider to derive the coarsest memoryless quantizer which can stabilize a single-input discrete-time linear time-invariant system with stochastic packet loss in the sense of stochastic quadratic stability. We show that the upper bound of the coarseness is strictly given by the packet loss probability and the unstable poles of the plants. We furthermore deal with permissible dead-zone width around the origin of the quantizers and time-varying finite quantizers in order to realize control using finite quantization steps.