On technical stability for sets of trajectories of discrete systems

The technical (practical) stability problem for a set of trajectories of discrete systems on a metric space of nonempty convex compact sets in $ \Bbb R ^ n $ is considered. On the basis of known results of convex geometry and comparison method, an approach of constructing the auxiliary Lyapunov functionals for the study of technical stability in terms of two measures of evolutionary equations with Hukuhara difference operator is proposed. The problem of estimating the solutions of equations is reduced to the study of finite-dimensional difference equations of comparison. Examples of technical stability study are given to illustrate the constructiveness of this approach.