Directed Information and Mutual Information in Linear Feedback Tracking Systems

Information transmission in discrete time LTI feedback tracking systems was investigated by using measures of directed information and mutual information. It was proved that, for pairs of extraneous input and internal variable, directed information (rate) is always equal to mutual information (rate); for pairs of internal variables, the former is smaller than the latter. Comparing the open-loop and closed-loop systems we got that, the feedback changes the information transmission between internal variables, while has no influence on information transmission from extraneous variables to internal variables. This is slightly different from the conclusion on communication channels. Consideration on system design was discussed