This paper proposes a novel structure of a power system stabilizer (PSS) to improve the stability of synchronous generators (SGs) in microgrids. Microgrids are relatively vulnerable in terms of stability due to their small size and low inertia. The rotational inertia and voltage support of SGs are highly suitable for getting over the vulnerabilities of microgrids, but there exist weaknesses in low-frequency oscillations (LFOs) and limitations of synchronization due to electromagnetic characteristics. Therefore, we study how to accommodate the features of microgrids in the PSS of SGs and further enhance present advantages. The PSS proposed in this paper not only damps out LFOs by conventional lead-lag compensation but also provides additional damping torque according to the magnitude of the perturbation using a synchronous impedance characteristic (SIC). The proposed Lyapunov energy-function-based control strategy can also increase the synchronizing power of the SG to improve transient stability. For performance verification, we use parameters obtained by the particle swarm optimization (PSO) algorithm to compare the existing PSS with the proposed one and analyze them. The effect of the proposed micro-power system stabilizer (µPSS) is analyzed through frequency response analysis, and finally, small-signal stability analysis and the performance of transient stability are verified by time-domain simulation (TDS) on MATLAB/Simulink.