Hello, Method is used in stability analysis is the limit equilibrium method is the widely used and accepted slope stability analysis method .

OR

1. Nyquisit criteria
2. Root locus method
3. Routh Hurwitz criteria

Slope stability analysis is a static or dynamic, analytical or empirical method to evaluate the stability of earth and rock-fill dams, embankments, excavated slopes, and natural slopes in soil and rock. Slope stability refers to the condition of inclined soil or rock slopes to withstand or undergo movement (https://en.wikipedia.org/wiki/Mass_wasting)

Hope it is helpful for you :)