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In an islanded microgrid, power electronic converters are used to exchange power, and these converters have very low inertia, thus compromising the frequency stability of the microgrid. Virtual inertia control is used to improve the frequency stability of an islanded microgrid. The derivative control technique is usually used to implement virtual inertia control in the microgrid. Factors such as disturbance and uncertainty of parameters of the islanded microgrid compromise the performance of virtual inertia control and may cause system frequency instability. Therefore, the virtual inertia control structure, a complementary controller is needed that can weaken the effect of disturbance on the microgrid as much as possible and be resistant to the uncertainty of parameters of the microgrid. In this paper, a robust control method is used in a virtual inertia control structure that uses system output feedback. The proposed method is expressed based on linear matrix inequality and is proved based on the Lyapunov criterion. Among the advantages of the proposed method is the attenuation of disturbance, resistance to the uncertainty of parameters of the microgrid, and increasing the degree of freedom to control the system in this method. The results of the proposed method to improve the performance of virtual inertia control in several different scenarios by considering the uncertainty of parameters of the two-zone microgrid and disturbances on the microgrid are compared with several methods and the effectiveness of the proposed method in terms of improving frequency stability is shown.