On some analysis and synthesis problems in general system theory

Problems of analysis and synthesis for a special kind of systems (manifolds) are discussed which often arise in applications of system theory. The manifold elements make a finite directed graph which satisfies a number of conditions. For a manifold without loops necessary and sufficient conditions are found for the family of manifold input — output relations to dictate its behaviour. The resultant conditions help analyze and synthesize manifolds without loops. An algorithm is developed which leads to that family and constructs any feasible set of non-intersecting paths from manifold.