Authors\´ reply [to comments on "control over noisy channels" by S. Tatikonda and S. Mitter]

The authors reply to the comment by A.S. Matveev and A.V. Savkin (see ibid., p.2105-10, 2005). We acknowledge the error pointed out in the comments, but wish to state that this was an oversight also missed by the referee of the paper. That one cannot observe an unstable process over a noisy channel in this strong sense has been known to us since at least 2000. Sahai´s Ph.D. dissertation (A. Sahai, 2001), written under the direction of one of the authors, investigates the information theory needed for unstable processes. There, he discusses the need for a weaker notion of stability (an appropriate moment stability). This led to the development of his anytime capacity framework. An explicit counterexample is given by A. Sahai (2001), showing that the result in question cannot be true. These ideas were further discussed by A. Sahai (2000; 2001) and Sahai and Mitter (2000). For plants without disturbances, S. Tatikonda and S. Mitter (2004) shows that the traditional Shannon capacity rate condition is sufficient to ensure stability over an erasure channel. The addition of plant disturbances requires a weaker notion of stability.