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This work presents the application of Linear Matrix Inequalities to the optimal adjustment of Power System Stabilizers with pre-defined structure, much common in the power industry. Results of some tests show that gain and zeros adjustments are sufficient to guarantee Power Systems robust stability and performance with respect to various points of operation. Making use of the flexible structure of LMI's, we propose an algorithm that permits one to choose in the compromise between low gain and high damping factor. The technique used here is the pole placement design together with gain limitation, which places the poles of the closed loop system in a specific region of the complex plane. Results of tests with a nine-machine system (New England -New York) are presented and discussed, in order to validate the algorithm proposed.