Various methods, devices and theoretical results related to the problem of applying information theory approaches to stochastic identification and robust control of systems are analyzed and discussed in detail. The use of recently published information theory criteria and entropy-based robust control results is examined and it is shown that these analyses lead to unexpected conclusions. In particular the use such an information-theoretic approach to the system identification as the minimum relative entropy principle is considered. Regarding the robust control problems, an approach is proposed based on the Tchebyshev type inequalities for random values, involving the case of unimodal probabilistic distributions, which is the most natural case in the applications.