A model-based decentralized control design and analysis is presented for varying topology ac autonomous microgrids. Particularly, the proposed method is developed on a modular form by considering local control schemes for each distributed generation (DG) region as it is formulated by a distributed energy resource (DER) among with its controlled power electronic interface and a local load. Each DG region is driven locally by a droop-based outer-loop slow control scheme in cascaded-mode with inner-loop fast current controllers. The proposed inner-loop current controllers are of simple proportional-integral (PI) type and do not involve the standard used parameter-depended decoupling terms. A general method of integrating the different DG regions, with their inner-loop fast controllers involved, is deployed to include any distribution network connecting the DG regions to each other and to external loads. To confront the challenging issue of proving stability and convergence to the desired equilibrium of such a complex, decentralized controlled microgrid, an advanced Lyapunov-based technique is effectively applied on the model constructed. Hence, the main novelty of the present approach is that it can be used as a flexible general tool, independently from the system scaling, parameters, operating conditions and the intermittent nature of the different DERs, since the modular and open model-based analysis enables expandability to any microgrid structure instead of considering all the DG units being connected in parallel or in a common bus. The overall scheme is evaluated by examining a typical stand-alone microgrid and the results verify the theoretical analysis indicating stability and smooth system performance without adverse impacts between the different parts.