Lyapunov function

A Lyapunov function is a mathematical tool used to determine the stability of a system, like a robot or an airplane, without solving complex equations. Think of it as an energy-like measure that decreases over time as the system moves toward a stable state. If this measure consistently drops and reaches a minimum, the system is stable—meaning it will settle into an equilibrium. It’s similar to how a ball rolls down a hill and eventually comes to rest at the lowest point; the Lyapunov function helps us understand and verify that behavior mathematically.