Lyapunov function

In the theory of ordinary differential equations (ODEs), Lyapunov functions are scalar functions that may be used to prove the stability of an equilibrium of an ODE. Named after the Russian mathematician Aleksandr Mikhailovich Lyapunov, who introduced them in his doctoral thesis General Problem of the Stability of Motion, the method of Lyapunov functions (also called the Lyapunov’s second method for stability) is important to stability theory of dynamical systems and control theory. Actually, it is the only universal method for the investigation of the stability of nonlinear dynamical systems of general configuration.