We investigate the controlled realization of a stable circular pursuit model in a multi-agent robotic system described by double-integrator dynamics with homogeneous controller gains. The dynamic convergence of the system starting from a randomly chosen, non-overlapping initial configuration to a sustained, stable pursuit configuration satisfying velocity matching and uniform inter-agent separation is demonstrated using the proposed control framework. The cyclic pursuit configuration emerges from local, linear, inter-agent interactions and is shown to be robust under stochastic perturbations of small and moderate intensities. The stability criterion discussed in this work is independent of the number of agents, permitting dynamic addition/deletion of agents without affecting overall system stability. Experimental results that validate the key theoretical results are also presented. Potential applications of the results obtained include cooperative perimeter tracking and resource distribution applications such as border patrol and wildfire monitoring.