In this article an H∞ -controller for an electrostatic micro-actuator (e-μA) whose model is linearized at multiple operating points, with structured uncertainty is presented. The (e-μA) is composed of a micro capacitor whose one plate is clamped while its other flexible plate's motion is constrained by hinges acting as a combination of springs and dashpots. The nonlinear model of the e-μA is linearized in multiple operating points with respect to the plates' displacement for the set of the resulting multiple operating models. A robust H∞-controller relying on LMI-theory is designed. The resulting controller stabilizes the set of linearized systems at the operating points despite the induced uncertainty. The proposed control scheme is applied on the nonlinear model of the e-μA, where the presented multiple simulation results prove the efficacy of the utilized controller.