A synthesis of a nonlinear discrete-time system having a periodic solution

In this paper a method of synthesis of a nonlinear discrete-time system having a periodic solution is investigated. Firstly, a system having a hypersurface, to which the solution trajectory starting from any initial point in the state space tends as time increases, is determined. Then, some conditions that the trajectory moves with a given period on this hypersurface are obtained. Finally, by considering the additional conditions, the system equation is determined. Some examples are shown.