On stabilizability of LTI systems across a Gaussian MAC channel

  • Liu J
  • Gupta V
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Abstract

In this paper, the problem of stabilizing two scalar plants across a Gaussian multiple access channel (MAC) is addressed. Both states are encoded separately and sent across a shared MAC channel to a joint decoder/controller. A necessary condition for stabilizing such a system in the mean square sense is obtained using information-theoretic tools. This condition establishes the relationship between the magnitude of the unstable eigenvalues and the capacity region of Gaussian feedback multiple-access channel. A time-division encoding scheme along with a switched linear control law is proposed to achieve a rate region that is sufficient for stabilizability. The problem is studied both under the assumption that the two encoders can cooperate by sharing information and that they cannot.

Author-supplied keywords

  • AWGN channels
  • Correlation
  • Decoding
  • Entropy
  • Gaussian MAC channel
  • Gaussian channels
  • Gaussian feedback
  • Information exchange
  • LTI systems
  • Transmitters
  • access protocols
  • decoding
  • eigenvalues
  • eigenvalues and eigenfunctions
  • information-theoretic tools
  • joint decoder/controller
  • mean square sense
  • switched linear control law
  • time-division encoding scheme

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Authors

  • J Liu

  • V Gupta

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