Lyapunov Methods

Lyapunov methods are mathematical tools used to analyze the stability of systems, such as mechanical or electrical systems, without solving complex equations fully. Think of them like a "stability gauge": if you imagine a ball in a bowl, Lyapunov functions help determine if the ball, when disturbed slightly, will return to the bottom (stable) or roll away (unstable). They involve constructing a special function that consistently decreases or remains steady over time, indicating the system’s tendency to stay close to equilibrium. This approach helps engineers ensure systems behave predictably and safely.