This paper discusses a new iterative method for designing power swing dampi
ng controllers. The method solves directly for a low-order robust controlle
r, and if convergence is achieved, results in the closed-loop system satisf
ying a frequency-domain bound. It is based on the optimization of dynamic s
ystems with linear matrix inequalities as the design constraints. Controlle
r constraints such as decentralization and positive realness can also be in
cluded in the design. The proposed method is used to design a power system
stabilizer for a single-machine infinite-bus system and a decentralized two
-channel series and shunt capacitor damping controller for a three-area sys
tem.