We consider a distributed control problem comprising of multiple sub-systems with one-controller at each sub-system. We apply a recent result about suboptimal receding horizon control that analytically relates a receding horizon control suboptimal solution and system performance loss to quantify the necessary number of iterations for the dual and primal decomposition algorithm to achieve a solution that guarantees stability. We also use this result to explore the idea of "incremental robustness", meaning that the overall system is robustly stable and its performance varies gracefully with the inclusion of sub-systems and sub-controllers. We demonstrate these ideas in a consensus seeking and a formation control problem and provide simulation results. To our best knowledge, this is the first time the result is applied to a distributed receding horizon control framework based on dual and primal decomposition.