Robust Entropy Rate for Uncertain Sources: Applications to Communication and Control Systems

In this paper the notion of robust entropy and subsequently, robust entropy rate for a family of discrete time uncertain sources is introduced. When the uncertainty is described by a relative entropy constraint between the set of uncertain source densities and a given nominal source density, the solution to this robust notion of information is presented and its connection with other notions of entropy definitions, such as, Renyi entropy and Tsallis entropy is presented. Then, the robust entropy rate is calculated for 1) Uncertain sources corresponding to a partially observed Gauss Markov process, 2) Sources with uncertain frequency response, and 3) Uncertain sources corresponding to a partially observed controlled Gauss Markov Process. Finally, an application of the robust entropy rate in networked control systems is presented by defining necessary conditions for uniform asymptotic stabilizability and observability.