As a supplement of the droop control, the concept of secondary controlled microgrid (MG) has been extensively studied for voltage and frequency restoration. However, the low band-width communication (LBC) channels are needed to exchange information between the primary and secondary controllers, and the performance of the secondary controller degrades due to the uncertain communication delay and data drop-out in the LBC lines. Recently, a washout filter-based power sharing method was presented without communication lines and additional control loops. In this paper, the equivalence between secondary control and washout filter-based power sharing strategy for islanded microgrid is demonstrated, and the generalized washout filter control scheme has been obtained. Additionally, the physical meaning of control parameters of secondary controllers is also presented. Besides, a complete small-signal model of the generalized washout filter-based control method for islanded MG system is built, which can be utilized to design the control parameters and analyze the stability of MG system. Finally, extensive simulation and experimental results are provided to confirm the validity and effectiveness of the derived equivalent control scheme for islanded MG.