Why did you choose this?
Because Lyapunov's stability theory is based on the viewpoint of energy, simply put, the energy of a system is constantly changing (increasing or decreasing) with the passage of time. In a limited time, the system tends to be stable and the energy is no longer changing.
At this point, the energy at k+ 1 minus the energy at k in our system is
This is Lyapunov stability theory.