Lyapunov Stability is a concept in control theory and dynamical systems that assesses the stability of an equilibrium point. An equilibrium point is considered stable if, when the system is slightly disturbed, it returns to that point over time. This is often analyzed using a function called a Lyapunov function, which helps determine whether the system's behavior remains close to the equilibrium.
If the Lyapunov function decreases over time, it indicates that the system is stable. Conversely, if the function increases, the system may be unstable. This method provides a systematic way to evaluate stability without needing to solve the system's equations directly.