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. The LMI optimization finds a control law that stabilizes several contingencies simultaneously using a polytopic model of the system. However, the number of cases to be considered is limited by computational complexity which increases the 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 the necessary polytopic control for a particular contingency and classifies the data as belonging to that polytopic domain. The technique has been tested on an 8-machine, 13 bus, system and has been found to give satisfactory results.