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This paper presents fundamental concepts of a central power-management system (PMS) and a decentralized, robust control strategy for autonomous mode of operation of a microgrid that includes multiple distributed energy resource (DER) units. The DER units are interfaced to the utility grid through voltage-sourced converters (VSCs). The frequency of each DER unit is specified by its independent internal oscillator and all oscillators are synchronized by a common time-reference signal received from a global positioning system. The PMS specifies the voltage set points for the local controllers. A linear, time-invariant, multivariable, robust, decentralized, servomechanism control system is designed to track the set points. Each control agent guarantees fast tracking, zero steady-state error, and robust performance despite uncertainties of the microgrid parameter, topology, and the operating point. The theoretical concept of the proposed control strategy, including the existence conditions, design of the controller, robust stability analysis of the closed-loop system, time-delay tolerance, tolerance to high-frequency effects and its gain-margins, are presented in this Part I paper. Part II reports on the performance of the control strategy based on digital time-domain simulation and hardware-in-the-loop case studies.