ABSTRACT. This paper concerns an output-tracking technique based on a standalone integrator with variable gain. The control algorithm, recently proposed by the authors, appears to have a wide scope in linear and nonlinear systems while aiming at simple and efficient computations in the loop. For a class of memoryless systems it resembles a Newton-Raphson flow for solving the loop equation, but it is applicable to a broader class of dynamical systems. Furthermore, the technique is suitable for tracking constant as well as time-dependent reference signals, and its convergence performance is robust with respect to computational errors in the loop. The objective of this paper is to test the technique on a control problem arising in multi-agent systems. Specifically, we are motivated by regulating trajectories of follower agents by a lead agent in a platoon or swarm of multi-agent networks connected by the graph Laplacian. We study a particular example, which is challenging from the standpoint of control, with the aim of identifying the limits of the technique and investigating their possible extensions.