Automatic voltage regulator (AVR) and power system stabilizer (PSS) as the most common excitation controllers have implemented incompatible decentralized control (IDC) due to the asynchronous sampling by the voltage/current transformer. However, IDC results in the incompatibility of decentralized AVR and PSS in regulating generator dynamics, which seriously reduces the capability of AVR and PSS in improving the power system stability. In this article, the concept of compatible decentralized control (CDC) based on synchronous local measurements is first proposed for the decentralized AVR and PSS to improve the power system stability. The mathematical models on IDC and CDC are, respectively, modeled to represent the compatible characteristics of CDC. The distinguishing feature of the proposed CDC is that the decentralized AVR and PSS can be compatible with one another in regulating generator dynamics. Simulation results on four IEEE benchmark systems show the advantages of CDC in improving power system stability compared with IDC.