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Stochastic Stabilization Over Noisy Channels

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Stochastic Networked Control Systems

Part of the book series: Systems & Control: Foundations & Applications ((SCFA))

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Abstract

This chapter investigates stochastic stabilization over erasure channels, discrete memoryless channels with and without feedback, and a class of continuous-alphabet channels. It is shown that for ergodicity (under additional technical assumptions), Shannon capacity with feedback provides a boundary condition in the space of communication channels for stochastic stabilization of unstable linear systems. For quadratic and finite moment stability, however, further conditions are required both on the channels as well as on the tail distributions of the system noise. The results include extensions to multi-dimensional and partially observed settings, and channels with memory.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, Queen’s University, Kingston, Ontario, Canada

    Serdar Yüksel

  2. Department of Electrical and Computer Engineering, Coordinated Science Laboratory, University of Illinois at Urbana-Champaign, Urbana, Illinois, USA

    Tamer Başar

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  1. Serdar Yüksel
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Yüksel, S., Başar, T. (2013). Stochastic Stabilization Over Noisy Channels. In: Stochastic Networked Control Systems. Systems & Control: Foundations & Applications. Birkhäuser, New York, NY. https://doi.org/10.1007/978-1-4614-7085-4_8

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