DC microgrid cluster (DCMGC) is a dynamic network formed by connecting a group of geographically neighboring DC microgrids (DCMGs) through tie-lines. Each DCMG collaborates with other DCMGs to achieve maximum economic benefits through flexible power flow management within the DCMG and at the system level. Therefore, DCMGCs require communication, computing, and control to manage the power flow. As a result, the DCMGCs are naturally represented as cyber-physical systems (CPSs). However, DCMGCs are of high penetration of distributed energy resources, which creates significant randomness at both resource and load sides. Consequently, these systems will experience large disturbances leading to serious stability problems like high oscillations or even collapse. In this paper, Takagi-Sugeno (T-S) modeling is utilized to reduce the large signal Lyapunov stability of DCMGs to a series of linear matrix inequalities (LMIs). The impact of key circuit parameters, control parameters, communication delay, and cyber-attacks on the large signal stability of DCMGCs is revealed, and the region of attraction (ROA) of the network is estimated as well. Finally, the large signal stability analysis is verified by experimental results. The findings of this work will be instrumental in developing more effective control strategies to enhance the stability and reliability of DCMGCs.