This paper presents a generalized linear model based on LMI state-feedbackwith integral action, applicable to the control of Electric Energy Stora-ge Systems (EESS) such as Superconducting Magnetic Energy Storage(SMES) and Supercapacitor Energy Storage (SCES). A Voltage SourceConverter (VSC) and a Pulse-Width modulated Current Source Converter(PWM-CSC) are respectively used to integrate the SCES and the SMESsystems to the electrical distribution system. To represent the dynamicsbetween the EESS and the power distribution system a reduced generallinear model in the state-space representation is introduced. The proposedcontrol scheme regulates independently the active and reactive power flowbetween the EESS and ac the grid. Three case scenarios comparing a con-ventional PI controller and the proposed technique are conducted conside-ring grid voltage fluctuations. Extensive time-domain simulations demons-trate the robustness and proper performance of the proposed controller to operate the EESS as power compensator, in order to improve the operativeconditions of electrical distribution systems.