Cooperation of connected vehicles is a promising approach for autonomous intersection control. This article presents a systematic approach to the cooperation of connected vehicles at unsignalized intersections without global coordination. A task-area partition framework is proposed to decompose the mission of cooperative passing into three main tasks, i.e., vehicle state observation, arriving time optimization, and trajectory tracking control. To accomplish these tasks, a distributed observation algorithm is introduced to achieve fixed-time observation of other vehicles' states for passing sequence determination, a distributed optimization algorithm is introduced to schedule conflict-free arriving times for trajectory planning, and a distributed control algorithm is proposed to address parameter mismatches and acceleration saturation for fixed-time trajectory tracking control. Numerical simulations demonstrate that the proposed method can achieve cooperative passing of vehicles without global coordination at the cost of a growth of 8.8-18.1% average travel times in low and medium traffic volumes.