This paper addresses the cooperative control problem of vehicular platoons on a loop road. By integrating speed-density relationship into the control strategy design, a novel distributed control protocol is proposed. The cooperative control problem is reformulated as a multi-agent consensus problem, which is further transformed into a partial stability problem through linear transformation. Using partial stability theory and the auxiliary system method, we derive a necessary and sufficient condition for solving the cooperative control problem. Finally, numerical simulations are conducted to verify the effectiveness of the proposed control scheme.