Integration of inverter-interfaced distributed generators (DGs), e.g., as microgrids, into traditional power systems, reduces the total inertia and damping properties, and accordingly increases uncertainty and sensitivity to the fault in the system. The concept of virtual synchronous generator (VSG) has been recently introduced in the literature as a solution that mimic the behavior of conventional synchronous generators in large power systems. Parameters of the VSGs are normally determined via comparing the virtual and the conventional synchronous generators. This paper introduces an extended VSG (EVSG) by combining the concept of virtual rotor, virtual primary and virtual secondary control. A H∞ robust control method is proposed for optimal tuning of the extended VSG parameters. A Microgrid test bench is used to verify the proposed control methodology.