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A multiple bifurcation phenomena is observed in a two-area example power system. A local bifurcation and an interarea bifurcation develop because of the multiple bifurcation parameter changes. The dynamic behaviors of the bifurcating system are complex due to the overlapping of the two different bifurcation subsystems and are shown to be difficult to control. The double bifurcations are studied And in order to stabilize them, three kinds of μ-synthesis robust controls are designed: 1) μ-synthesis power system stabilizer (MPSS); 2) μ-synthesis SVC control (MSVC); and 3) a mixed MPSS/MSVC control. Based on the bifurcation subsystem analysis, the measurement signals and locations of the controls are selected. The control performances and the RGA matrix information of three kind of controls are compared. The conclusions are given according to the analysis and time simulation results.