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For the first time, we apply the sum-of-squares (SOS) decomposition technique for robust control of power systems. We propose an SOS L2 robust control scheme aiming at a power system characterized by exogenous disturbances. A set of states-related inequalities are utilized to guarantee L2 gain disturbance attenuation performance of the system. It involves semidefinite programming relaxations based on the SOS decomposition technique, which is employed to solve the inequalities that bring about robust control of the system. This method is superior to other traditional approaches. It is able to construct a robust controller that guarantees L2 gain disturbance attenuation performance of the system featuring exogenous disturbance by the SOS algorithm without solving Hamilton-Jacobi inequalities or using the recursive design of back-stepping. Then, the proposed approach is applied to derive a robust excitation controller for multimachine power systems. Moreover, a three-machine power system model is employed to test the robust excitation controller, which finally verifies its effectiveness and superiority. © 2017 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc. [ABSTRACT FROM AUTHOR]