Bounded Perturbations of Nonlinear Discrete Systems: Estimation of Impact and Minimization

The problem of minimizing the impact of bounded perturbations on certain classes of controlled nonlinear discrete systems is solved. The radius of the invariant set, an analog of variance for the perturbations of probabilistic nature, is taken as a measure of the impact. The cases of two-sided linear and nonlinear constraints that form multivalued mappings and also the case in which the nonlinear function has a given estimate of the norm are...