Control of Multi-Dimensional Linear Systems over Noisy Forward and Reverse Channels

We consider the problem of stabilizability of remote continous-time multi-dimensional LTI systems where both the forward (from the sensor to the controller) and the reverse (from the controller to the plant) channels are noisy and memoryless. By adopting an information theoretic approach, and using the theory of Markov processes, we obtain necessary and sufficient conditions for stabilizability, with the conditions being on channels, coders, and controllers. We show that the entire state and control spaces have to be encoded to obtain an invariant probability distribution, which leads to the necessity of using variable length codes in the case of discrete memoryless channels. We introduce a stabilizing variable length coding scheme through variable rate sampling of the continuous-time system. Control over continuous memoryless channels is also considered.