Lyapunov's stability theorem

Lyapunov's stability theorem is a concept in mathematics and engineering that helps us understand the behavior of systems over time. It states that if you have a system (like a pendulum or an airplane) that returns to a stable condition after small disturbances, it is considered stable. The theorem provides a way to analyze whether a system will stay close to this stable state, even when faced with minor changes. Essentially, it helps predict whether a system will remain balanced or deviate dangerously from its intended path.