An Information-theoretic Interpretation of Stability and Observability

Many dynamical models which have been analyzed in the context of system theory, can also be viewed as communication channels with memory. In this interpretation, the system's input is a transmitted message and the observation, or output, is the received message. Information-theoretic measures like entropy, mutual information and capacity can therefore be employed, and key concepts in system thery, such as observability, controllability and stability, can be expressed in information-theoretic terms. In this paper we study certain linear Markovian models from this viewpoint Observability of a Markovian linear discrete-in system is shown to be related to entropies of the initial state and the output observation. Stability is found to pertain to the capacity of the channel which represents the system. The derived relations expose the role of information flow in dynamical system behavior and suggest applications for other liner and nonlinear models.