A nonstochastic information theory for feedback

This paper extends a recently proposed theory of nonstochastic maximin information to study feedback systems with erroneous channels. The concepts of conditional and directed maximin information are introduced, without assuming any statistical structure. It is proved that the zero-error feedback capacity of a stationary memoryless channel coincides with the largest rate of directed maximin information across it. This provides a nonstochastic counterpart to recent results in information theory. This characterization is then used to find a tight condition for exponential uniform stabilizability of a linear time-invariant plant over an erroneous channel, consistent with a result of Matveev and Savkin.