Stochastic feedback and its relation to the entropy criterion

In this paper, we generalize the interpretation of the entropy criterion by using stochastic feedback. When a common white Gaussian noise of zero mean and unit variance is applied, the entropy of a transfer function is shown to be equivalent to the maximum variance of the outputs fed back and added to the input through multiplication of a stochastic gain. It turns out that the existing minimum entropy control is useful for minimizing the worst effect of external noises on the outputs when stochastic feedback is applied.