Escape time formulation of state estimation and stabilization with quantized intermittent communication

The problems of state estimation and feedback stabilization of a linear 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 system output from a specific domain. The complications introduced by communications–intermittency, channel noise, quantization, etc.–are evaluated using a Markov stopping time formulation. This is compared to and contrasted with earlier analyses which considered the behavior of Kalman filters with intermittent data based on moments and conditional moments, and the evaluation of the minimal number of bits required for mean square stabilization. The main result shows the escape time is characterized by a Markov chain which is amenable to explicit analysis through the calculation of its cumulative distribution function. This is examined in the linear Gaussian and quantized linear Gaussian cases and then used to develop an approach to bitrate assignment in such communications-based control systems.