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In this paper, the power system model is formulated as a finite dimensional linear system whose state-space entries depend continuously on a time varying parameter vector called the scheduling variables. This system is referred to as the linear parameter varying (LPV) system. Although the trajectory of the changing parameters such as load levels and tie line flows is not know in advance, in most situations, they can be measured in real time. The LPV technique is applied to the decentralized design of power system stabilizers (PSS) for large systems. In the approach developed, instead of considering the complete system model with all the interconnections, we develop a decentralized approach where each individual machine is considered separately with arbitrarily changing real and reactive power output in a defined range. These variables are chosen as the scheduling variables. The designed controller automatically adjusts its parameters depending on the scheduling variables to coordinate with change of operating conditions and the dynamics of the rest of the system. The resulting PSSs give good performance in a large operating range. Design procedures are presented and comparisons are made between the LPV decentralized PSSs and conventionally designed PSSs on the 50-generator IEEE test system.