Escape time formulation of state estimation and stabilization with intermittent communication

The problems of state estimation and feedback stabilization of an unstable system including a communications channel are quantified as escape or survival times, which yield stochastic processes describing the time of first exit of the state estimate error or of the state itself from a specific domain. The system complications introduced by communications - intermittency, channel noise, etc - are evaluated using a Markov hitting time formulation. This is compared to and contrasted with earlier analyses which considered: the behavior of Kalman filters with intermittent data, the evaluation of the minimal number of bits required for mean square stabilization, and the Large Deviations analysis of probability theory. The main result shows the the escape time is characterized by a Markov chain which is amenable to explicit analysis in the linear gaussian case.