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The international thermonuclear experimental reactor (ITER) is the next step toward the realization of electricity-producing fusion power plants. ITER has been designed so as to reach the plasma burning condition, and to operate with high elongated unstable plasmas. However, due to the constraints which affect the machine realization, these open-loop unstable high performance plasmas can be hardly stabilized using the Poloidal Field coils placed outside the tokamak vessel. In this paper, it is proposed to use the in-vessel coils to vertically stabilize the plasma. In particular a constraint on the current in the in-vessel coils is explicitly taken into account in the design procedure, so as to yield a controller which can operate safely. Furthermore, the proposed controller is designed as a static-output feedback, in order to obtain a simple structure which permits to envisage effective adaptive algorithms, as it is usually required in operating tokamaks. The sufficient condition provided to design the controller is expressed in terms of a Bilinear Matrix Inequalities feasibility problem. The effectiveness of the approach is shown in a study case.