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In order to reduce the detrimental effects of inter-area oscillations on system stability, it is possible to use Linear Matrix Inequalities (LMIs) to design a multi-objective state feedback control. The LMI optimization comes up with a control law that stabilizes numerous operating conditions simultaneously using a polytopic model of the system. However, the number of cases to be considered is limited by computational complexity and increased chances of infeasibility. In order to circumvent this problem, this paper presents a method for solving multiple polytopic problems having a common base case. The proposed algorithm determines which polytopic control is necessary for a particular contingency and classifies them as belonging to that polytopic domain. The technique was tested on an 8-machine, 13 bus system and provided satisfactory results.