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This paper addresses the problem of distributed secondary control for islanded AC microgrids with external dis-turbances. By using a full-order sliding-mode (FOSM) approach, voltage regulation and frequency restoration are achieved in finite time. For voltage regulation, a distributed observer is proposed for each distributed generator (DG) to estimate a reference voltage level. Different from some conventional observers, the reference voltage level in this paper is accurately estimated under directed communication topologies. Based on the observer, a new nonlinear controller is designed in a backstepping manner such that an FOSM surface is reached in finite time. On the surface, the voltages of DGs are regulated to the reference level in finite time. For frequency restoration, a distributed controller is further proposed such that a constructed FOSM surface is reached in finite time, on which the frequencies of DGs are restored to a reference level in finite time under directed communication topologies. Finally, case studies on a modified IEEE 37-bus test system are conducted to demonstrate the effectiveness, the robustness against load changes, and the plug-and-play capability of the proposed controllers.