This article's objective is to propose a decentralized one Degree of Freedom (DoF) robust control system with H∞ performance criteria for optimal voltage control of an uncertain inverter-interfaced AC microgrid in the islanding mode of operation. The islanded microgrid system comprises multiple Distributed Generation (DG) units connected with general topology. The proposed one DoF voltage control system provides robust performance alongside robust stability against various sources of uncertainty, such as local load variations, Plug-and-Play (PnP) operation of the DG units, topology variations, and different subsequent changes. To that end, first, each DG unit is modeled as a Linear Time-Invariant (LTI) system with a new polytopic type uncertainty. Next, a Linear Matrix Inequality (LMI) based state-feedback control system with H∞ performance criteria is implemented on the LTI polytopic islanded microgrid system. The controller's decentralized structure excludes the need for communication channels, and the controller's robust performance characteristic eliminates the necessity of pre-filter design. Simulating multiple scenarios in MATLAB/SimPowerSystems Toolbox confirms the developed controller's performance in different scenarios, including voltage tracking, local load changes, PnP operation, and topology changes.
