  In this paper, we show through examples, how the existing definitions of
information transfer, namely directed information and transfer entropy fail to
capture true causal interaction between states in control dynamical system. We
propose a new definition of information transfer, based on the ideas from
dynamical system theory, and show that this new definition can capture true
causal interaction between states. The information transfer measure is
generalized to define transfers between the various signals in a control
dynamical system and analytical expression for information transfer between
state-to-state, input-to-state, state-to-output, and input-to-output are
provided for linear systems. There is a natural extension of our proposed
definition to define information transfer over $n$ time steps and average
information transfer over infinite time step. We show that the average
information transfer in feedback control system between plant output and input
is equal to the entropy of the open loop dynamics thereby re-deriving the Bode
fundamental limitation results using the proposed definition of transfer.
