This paper presents a strategy for dynamic stability analysis of hybrid islanded DC microgrids using nonlinear backstepping controllers (NBCs) with different microgrid components. The main components of the DC microgrid are a solar photovoltaic system, a diesel generator with rectifier, loads, and a battery energy storage system. In this paper, the controller is designed to control the output power of these components as well as to minimize the mismatch between the generation and consumptions while maintaining a constant DC-bus voltage where all microgrid components are directly or indirectly connected to this DC-bus through power electronic interfaces. The proposed NBC is designed recursively based on the Lyapunov theory for each component of the microgrid. The overall stability of the whole DC microgrid is analyzed through the formulation of control Lyapunov functions (CLFs) during the different stages of the design process and the theoretical stability is ensured through the negative semidefiniteness of the derivative of CLFs. The effectiveness of the proposed controller is evaluated on a hybrid DC microgrid under different operating conditions and compared with a nonlinear sliding mode controller (SMC). Simulation results demonstrate the superiority of the proposed control scheme over the SMC in terms of achieving steady-state operating conditions.