Lyapunov stability

Lyapunov stability refers to the idea of how a system responds to small disturbances. When a system is considered Lyapunov stable, it means that if it is slightly disturbed from its original state, it will return to that state and remain close to it over time. Imagine a marble in a bowl: if you slightly nudge the marble, it will roll but eventually settle back in the bowl. In contrast, if a small nudge causes the marble to roll out of the bowl, the system is unstable. Lyapunov stability helps in analyzing the reliability of dynamic systems in various fields, including engineering and physics.