Increasing expansion of power systems is accompanied by innovations in smart grid solutions to maintain system stability. This paper formulates the dual-dimensional supplementary damping controller (SDC) and accelerating power system stabilizer (PSS2B) design as a multi-objective optimization procedure including both performance and robustness criteria. In wide-area operation, PSS2B is used for damping low-frequency swings and maintaining the robustness of controller in a wide range of swing frequencies. A dual-dimensional controller model is employed for the SDC. The robustness requirement is procured by using the idea of pseudospectra to handle the changes of power system parameters and the time delay introduced by wide-area damping controller (WADC). The multi-objective optimization problem is solved using an improved non-dominated sorting genetic algorithm-II (INSGA-II) based on fuzzy decision making (FDM) method. Different simulations are carried out on a 4-machine 2-area test system in order to validate the effectiveness and robustness of the designed controllers.