We consider a set consisting of an arbitrary number of conservative systems of arbitrary orders. It is assumed that each of the systems admits a nondegenerate family of single-frequency periodic motions and the whole set of systems considered as one conservative system has the same property. We assume that oscillations of one period in each system have individual phase shifts. The problem of aggregating a coupled system with an attracting cycle is solved. We choose a leader conservative system, which becomes a closed-loop system through van der Pol dissipation-type feedback in order to implement an attracting cycle. The next (follower) conservative system is connected to the leader one through a unidirectional coupling control. Van der Pol dissipation is applied in such a way that the coupled system also has an attracting cycle. Further, each subsequent system joins the previous system: a chain of weakly coupled conservative systems with an attracting cycle is aggregated. In the chain, the previous system, as the leader, acts on the subsequent system, as the follower, through a unidirectional coupling control. The selected coupling controls are universal and can be applied to any conservative systems that satisfy the stated assumptions. A numerical example of the formation of a chain of three identical mathematical pendulums, which are aggregated by the proposed method into a chain of weakly coupled systems with an attracting cycle, is given.