Control of Discrete-Time Partially-Observed Jump Linear Systems Over Causal Communication Systems

We consider the problem of control of discrete-time partially-observed jump linear system over a noisy causal communication channel. Necessary conditions for observability and stabilizability in probability and r-th mean of a jump linear system driven by a Markov chain are derived. The methodology is information theoretic and it is based on an alternative definition of mutual information between two random processes which is restricted to a causal channel. Specifically, the self-mutual information is restricted to Radon-Nykodym derivatives corresponding to causal channels. This gives rise to information capacity and rate distortion formulaes which involve causal operations, leading to a new set of data processing inequalities