This paper studies the cooperative estimation control framework of a DC microgrid (DC-MG) system based on a T-S fuzzy model under the hybrid attacks of denial of service (DoS) and false data injection (FDI). The T-S model of the DC-MG system is established considering the non-uniform time scale of parallel distributed compensation (PDC) fuzzy control rules and the networked T-S fuzzy model. In order to relax the requirement that existing DoS attack models usually assume that the attack frequency and duration are limited, a new DoS attack model is proposed within the known range of the sleep and active periods of the attack signal. At the same time, a switching pulse observer is constructed to estimate the unknown FDI attack signal generated by the external dynamic system. Then, using the time-varying Lyapunov function method depending on the attack parameters, the exponential stability criterion of the system under hybrid attacks is derived. In addition, a joint design method of the fuzzy controller and the FDI attack observer based on linear matrix inequality is presented. Finally, the effectiveness of the proposed theoretical results is verified by a case study.