Pichkur V. Analysis and estimation of differential inclusions using methods of practical stability

The main purpose of the investigation is to evolve the theory of practical stability of differential inclusions. In this thesis a class of space-even set-valued mappings is defined. It is proven that for such mappings from upper semi-continuity the inner point of an image remains inner in some neighbourhood of an argument. The definition of a tube of a set-valued function is given. It is shown that for the upper semi-continuous space-even set-valued mapping its tube consists of points lying on the image boundary.Four types of practical stability of differential inclusions (inner strong, inner weak, external strong, external weak) are defined.The author gives conditions in which a point belongs to the boundary of the maximal by inclusion set. It is shown that the maximal by inclusion set of practical stability continuously depends on phase restrictions and the time interval. Algorithms for calculating optimal sets of initial conditions are offered.Basing on the theory of practical stability different applied problems are analysed.