A Lyapunov Function is a mathematical tool used in stability analysis of dynamical systems. It is a scalar function that helps determine whether a system will converge to a stable equilibrium point over time. If the function decreases along the trajectories of the system, it indicates stability. In control theory, Lyapunov Functions are essential for designing controllers that ensure system stability. They are named after the Russian mathematician Alexandre Lyapunov, who developed this concept in the late 19th century. By finding an appropriate Lyapunov Function, engineers can assess and guarantee the performance of various systems, from mechanical to electrical.