The Lyapunov Function

A Lyapunov function is a mathematical tool used to analyze whether a system, like a mechanical or electrical one, will settle into a stable state over time. Think of it as an energy-like measure that always decreases as the system approaches equilibrium, similar to how a ball rolls downhill to a resting point. If such a function exists and steadily decreases, it indicates the system is stable—returning to equilibrium after small disturbances. Lyapunov functions help control engineers and scientists ensure systems behave predictably and don't diverge into chaotic states.