Periodic behaviors in multi-agent systems with input saturation constraints

In this paper, we give conditions for the existence of periodic behaviors in a multi-agent system of identical discrete-time double integrators with input saturation constraints. If the feedback gain parameters of the controllers, which are based on relative state measurements of the agent itself and its neighboring agents, are bounded by a value depending on the largest eigenvalue of the Laplacian matrix, then the multi-agent system exhibits a periodic solution for certain initial conditions.