This paper presents a generalized linear model based on LMI state-feedback with integral action, applicable to the control of Electric Energy Storage Systems (EESS) such as Superconducting Magnetic Energy Storage (SMES) and Supercapacitor Energy Storage (SCES). A Voltage Source Converter (VSC) and a Pulse-Width modulated Current Source Converter (PWM-CSC) are respectively used to integrate the SCES and the SMES systems to the electrical distribution system. To represent the dynamics between the EESS and the power distribution system a reduced general linear model in the state-space representation is introduced. The proposed control scheme regulates independently the active and reactive power ow between the EESS and ac the grid. Three case scenarios comparing a conventional PI controller and the proposed technique are conducted considering grid voltage uctuations. Extensive time-domain simulations demonstrate the robustness and proper performance of the proposed controller to operate the EESS as power compensator, in order to improve the operative conditions of electrical distribution systems.