This study proposes a fully decentralized secondary voltage control scheme which employs the state estimation method in autonomous microgrids. Based on a large-signal dynamic model of a microgrid, a linear parameter varying based state estimator that is localized in each distributed generation (DG) unit serves as an alternative communication role and obtains the dynamics of the other DG units independently. A linear matrix inequality formulation for pole placement condition is derived for the state estimator design. A decentralized secondary voltage controller is, thus, able to achieve accurate reactive power sharing and average voltage restoration without any additional communication links. Our approach offers superior reliability, flexibility, and economic efficiency because of the irrelevance of communications to its performance, which is essential when conventional centralized or distributed methods are likely to yield towards poor performance or even instability under communication latency or data drop-out conditions. Simulation results that verify the effectiveness of the proposed methodology are provided.