Localy stable discrete control systems

Discrete-time systems referred to as locally stable, LS systems, are generalizations of control systems with a Lyapunov-stable continuous part. A subclass of coarse LS systems is isolated in which all motions tend to certain periodic motions including all steady-state processes in such systems. Coarseness is found to be a typical property of LS systems whose structure of motions is completely determined by a certain directed graph: in systems whose directed graphs are analogous this structure is in a sense equaivalent. Algorithms for design of a directed graph are illustrated with a second-order relay system as an example.