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 used, and key concepts in system theory, such as observability, controllability and stability, can be expressed in information-theoretic terms. The authors study certain linear Markovian models from this viewpoint. Observability of a Markovian linear discrete-time 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 linear and nonlinear models.