Chaotic disturbance rejection a Kolmogorov-Sinai entropy approach

This paper deals with disturbance rejection, when the external disturbance signal is a chaotic process. The authors measure the amount of chaos by the Kolmogorov-Sinai entropy. The natural question is the extent to which the Kolmogorov-Sinai entropy is reduced by means of a feedback. The answer is that it is not possible to reduce the Kolmogorov-Sinai entropy to a measure feedback if the closed loop measure preserving, i.e., conservative, system is stable and minimum phase. Moreover, if the external disturbance signal is a stochastic process, then, in general, the Shannon entropy rate does not decrease because of the Bode limitation.<>