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This paper presents an application of probabilistic theory to coordinated design of power system stabilizers (PSSs) and FACTS controllers, taking static VAr system (SVC) as an example. The aim is to enhance the damping of multi electromechanical modes in a multimachine system over a large and pre-specified set of operating conditions. In this work, conventional eigenvalue analysis is extended to the probabilistic environment in which the statistical nature of eigenvalues corresponding to different operating conditions is described by their expectations and variances. Probabilistic sensitivity indices (PSIs) are used for robust damping controller site selection and initial parameter setting. A probabilistic eigenvalue-based objective function for coordinated synthesis of PSS and SVC controller parameters are then proposed. The effectiveness of the proposed controllers is demonstrated on an 8-machine system.