Power system stability characteristics are typically evaluated in terms of small- and large-signal (transient) stability. Access to the time-varying A-matrix of a state-space-based power systems model during transient conditions can be utilized to apply Linear Time-Varying (LTV) system concepts for large-signal stability analysis. In LTV system analysis, the differential Riccati equation (DRE) plays a vital role when the power system is subjected to a severe disturbance. The Möbius transformation is proposed in this paper to solve the DRE with singularity issues. It is shown that the solution of the DREs follows a specific mathematical pattern when the power system is stable but does not follow this pattern when the system progresses toward instability. The proposed method can be used in large-signal stability analysis to predict instability and make the stability analysis more efficient. Additionally, the vector-differential Riccati equation (V-DRE) is proposed to generalize the index in a large-scale power system. Results show that analyzing the corresponding Riccati equation’s behavior can help researchers predict a power system’s performance and improve the control and management of the system.