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Power systems are under greater stress today due to the rapid growing demand and market-oriented activities. Operation of the existing system networks is gradually approaching their transmission limits and this raises a lot of stability problems which could potentially result in series consequences. The advent of FACTS provides new solutions to the reinforcement of the existing networks. Furthermore, the integration of FACTS also creates additional opportunities for the enhancement of system dynamic stability. This thesis presents the robust damping control of power systems with FACTS for the purpose of improving system small-signal dynamic stability. A Novel BMI-based methodology is proposed for the design of robust FACTS damping controllers. Different from most of the existing method, the proposed method is capable of managing multiple control objectives under several preselected operating points which could guarantee controller robustness in a broader range. The generality and feasibility of the proposed method is validated by controller designs on a two-area four-generator system and a five-area 16-generator 68-bus system with different FACTS devices. As an extension of the proposed BMI-based method, a coordinated design approach for multiple FACTS damping controllers is developed to address the damping problem with respect to multiple dominant oscillatory modes in large interconnected power systems. To reduce the adverse interactions between different FACTS devices, multiple SISO controllers are designed in a sequential manner with cautiously selected feedback signals. The coordinated design approach is then applied on a five-area 16-generator 68-bus system with an SVC and a TCSC to evaluate its effectiveness.