The Necessity and Sufficiency of Anytime Capacity for Stabilization of a Linear System Over a Noisy Communication Link—Part I: Scalar Systems

@article{Sahai2006TheNA,
  title={The Necessity and Sufficiency of Anytime Capacity for Stabilization of a Linear System Over a Noisy Communication Link—Part I: Scalar Systems},
  author={Anant Sahai and Sanjoy K. Mitter},
  journal={IEEE Transactions on Information Theory},
  year={2006},
  volume={52},
  pages={3369-3395}
}
In this paper, we review how Shannon's classical notion of capacity is not enough to characterize a noisy communication channel if the channel is intended to be used as part of a feedback loop to stabilize an unstable scalar linear system. While classical capacity is not enough, another sense of capacity (parametrized by reliability) called "anytime capacity" is necessary for the stabilization of an unstable process. The required rate is given by the log of the unstable system gain and the… CONTINUE READING
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