Lyapunov's Direct Method

Lyapunov's Direct Method is a way to analyze whether a system will settle into a stable state without solving its exact equations. It involves finding a special function, called a Lyapunov function, that acts like an energy measure, decreasing over time as the system evolves. If such a function can be found and it always decreases except at one point, it indicates the system naturally moves toward that point, showing stability. This method helps engineers and scientists determine system stability efficiently, especially when solving equations directly is difficult.