Focusing on the instability of mixed traffic flow including connected vehicles and traditional vehicles, this paper proposes an analytical method for the asymptotic stability of the mixed traffic flow with connected vehicles. Based on the transfer function theory, the car-following models were used to derive the transfer function of disturbances spreading in traffic flow. Then the analytical framework of asymptotic stability of mixed traffic flow was built under different proportions of connected vehicles. The intelligent driver model (IDM) and optimal velocity model (OVM) were selected as car-following models for connected vehicles and traditional vehicles, respectively. Subsequently, case analysis of asymptotic stability of mixed traffic flow was conducted and numerical simulations were performed under small disturbances. Results showed that the proposed analytical framework of asymptotic stability of the mixed traffic flow can be used to calculate the stability region of the mixed traffic flow related to connected vehicle proportion and equilibrium velocity. When the equilibrium velocity was larger than 21.5 m·s^-1, the mixed traffic flow was stable under any connected vehicle proportion. When the connected vehicle proportion was larger than 0.63, the mixed traffic flow was stable under any equilibrium velocity. Moreover, the numerical simulation experiments of mixed traffic flow validated the soundness of the theoretical analysis. The analytical framework of asymptotic stability of mixed traffic flow can be applied to different car-following models. It can also be used to analyze impacts of connected vehicles on traffic flow stability under the condition of real experimental tests.