The admissibility of periodic processes and existence theorems for periodic solutions. I (Q1390438)

The first part of the paper which consists of two parts is devoted to the admissibility of periodic processes. Admissibility means that to any periodic control from a fixed set there corresponds a periodic solution, which is situated in a domain of a phase space given beforehand. The property of admissibility is of importance in problems of control and guidance of periodic motions. It enables one to elucidate domains of a priori location of periodic solutions to nonlinear systems of differential equations. This first part consists of two sections. The first section deals with a concrete mathematical model which describes a nonstationary process in a chemical reactor. A theorem which gives conditions and domains of periodic oscillation is formulated. In the second section some criteria are discussed for the admissibility of linear systems of differential equations. Several examples are given. The proofs of the first section and some of the proofs of the second section are moved to the second part of the paper.