We propose a fully distributed control system architecture, amenable to in-vehicle implementation, that aims to safely coordinate connected and automated vehicles (CAVs) in road intersections. For control purposes, we build upon a fully distributed model predictive control approach, in which the agents solve a nonconvex optimal control problem (OCP) locally and synchronously, and exchange their optimized trajectories via vehicle-to-vehicle (V2V) communication. To accommodate a fast solution of the nonconvex OCPs, we apply the penalty convex-concave procedure which aims to solve a convexified version of the original OCP. For experimental evaluation, we complement the predictive controller with a localization layer, being in charge of self-localization and the estimation of joint collision points with other agents. Moreover, we come up with a proprietary communication protocol to exchange trajectories with other agents. Experimental tests reveal the efficacy of proposed control system architecture.