The Lyapunov stability criterion is a method used in control theory and dynamical systems to determine the stability of an equilibrium point. It assesses whether small disturbances in a system will decay over time, allowing the system to return to its equilibrium state. If a system is stable, it means that any small changes will not lead to large deviations from this point. To apply the criterion, a Lyapunov function is constructed, which is a scalar function that helps analyze the system's behavior. If this function decreases over time, it indicates that the system is stable. Conversely, if the function increases, the system may be unstable.