DC microgrids (DCMGs) are made up of a network of sources and loads that are connected by a number of power electronic converters (PECs). The increase in the number of these PECs instigates major concerns in system stability. While interconnecting the microgrids to form a cluster, the system stability must be ensured. This paper proposes a novel step-by-step system matrix building (SMB) algorithm to update the system matrix of an existing DCMG cluster when a new microgrid is added to the cluster through a distribution line. The stability of the individual DCMGs and the DCMG cluster is analyzed using the eigenvalue method. Further, the particle swarm optimization (PSO) algorithm is used to retune the controller gains if the newly formed cluster is not stable. The simulation of the DCMG cluster is carried out in MATLAB/Simulink environment to test the proposed algorithm. The results are also validated using the OP4510 real-time simulator (RTS).