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The study presents a method for the coordinated design of low-order robust controllers for stabilising power system oscillations. The design uses conic programming to shift under-damped or unstable modes into a region of sufficient damping of the complex plane and involves two stages. The first stage is a phase compensation design that accounts for multiple operating conditions with flexible AC transmission systems (FACTS) and power system stabilisers (PSS), unlike our earlier approach involving PSS only. The second stage is gain tuning. This is done effectively in a coordinated way using conic programming. An example demonstrates the method's ability to design coordinated FACTS and PSS controllers resulting in damping oscillations over all given operating conditions of the power system with very simple and low-order control structure.