Application of the Lyapunov vector functions to the stability study of fixed points in the sets of discrete dynamic systems

Stability conditions for fixed points of the dynamic systems in the space of nonempty convex compacts in finite-dimensional space were obtained. For the sets of dynamic systems, a methods was proposed to construct the Lyapunov vector functions. The study was carried out using the Matrosov method of comparison in combination with the methods of the convex geometry. In some special cases, the results obtained are applicable to the study of the sets of trajectories of dynamic systems.