Properties of nonlinear confidence estimates for statistically uncertain systems

Consideration is given to the problem of confidence estimation for statistically uncertain systems with observation, i.e., for systems in the description of which there are both random perturbations with known distributions and unknown perturbations with the information only about domains of their possible values. Confidence estimates for a state of the system are designed according to the earlier proposed method based on the use of random information sets. The behavior of confidence sets when variances of nonrandom perturbations tend to zero and sets of uncertainty of random perturbations contract to a point is studied.