The paper deals with the design and simulation of control systems for an unstable plasma vertical position of the linear model using Linear Matrix Inequalities (LMI) approach. It is necessary to suppress minor disruptions and stabilize a system output during a plasma discharge. The problem of state feedback stabilization for different LMI regions (left half-plane, vertical strip region, and intersection of sector and left half-plane) has been solved, as well as a state feedback LMI controller has been designed, and the systems have been simulated. In addition, a mixed system with desired pole region placement has been designed and modeled. The derived control systems and a modal system with three-time multiple pole were compared in the numerical simulations on the base of a control energy criterion. The estimation of the acceptable disturbance in the presence of the plant input-output constraints was done by means of ellipsoid techniques.