The paper aims to ensure that traffic parameters are simultaneously available between sparse sensors, and to improve the traffic efficiency of expressways and achieve the consistent driving state of mixed vehicle groups. Firstly, we propose a dynamic mixed segmental linear (DMSL) traffic model with external disturbances including automated vehicles (AVs) and connected automated vehicles (CAVs) as the composition of mixed vehicle groups on the expressway. Secondly, an observer-based double closed-loop control strategy is investigated by jointly controlling the on-ramp flow in the outer-loop control system and the driving state of mixed vehicle groups on the main section of the expressway in the inner-loop control system. Thirdly, the convergence and stability of the inner-loop control system and the outer-loop control system are analyzed by using Lyapunov stability theory, and the control gain and observation gain of the double closed-loop are obtained via adopting linear matrix inequality (LMI) method. Finally, numerical simulation experiments are executed to confirm the feasibility and accuracy of the proposed control algorithm. The results illustrate that the proposed control method is effective while the percentage of automated vehicles (AVs) is gradually increasing.