Lyapunov stability is a concept in control theory and dynamical systems that describes the behavior of a system near an equilibrium point. A system is considered stable if, when slightly disturbed, it returns to its original state over time. This means that small changes in the initial conditions do not lead to large deviations in the system's behavior. To analyze stability, Lyapunov's direct method uses a function called a Lyapunov function. This function helps determine whether the system will remain close to the equilibrium point. If the Lyapunov function decreases over time, it indicates that the system is stable, providing a mathematical way to assess stability without solving the system's equations directly.