A Mathematical Framework for Robust Control Over Uncertain Communication Channels

In this paper, a mathematical framework for studying robust control over uncertain communication channels is introduced. The theory is developed by 1) Generalizing the classical information theoretic measures to the robust analogous, which are subject to uncertainty in the source and the communication channel, 2) Deriving a lower bound for the robust rate distortion, and 3) Finding a necessary condition on the communication blocks subject to uncertainty for reliable communication up to distortion level Dv. By invoking this mathematical framework, necessary conditions for uniform asymptotic observability and stabilizability are derived for the following uncertain plants controlled over uncertain communication channels. 1) A probabilistic uncertain plant defined via a relative entropy constraint and 2) A frequency domain uncertain plant defined via an H^∞constraint.