Lyapunov function

In the theory of dynamical systems, and control theory, Lyapunov functions, named after Aleksandr Mikhailovich Lyapunov, are a family of functions that can be used to demonstrate the stability of some state points of a system.

The demonstration of stability require finding a Lyapunov function for that system. Not finding one such function does not prove stability or instability, so nothing can be said. There is no direct way to obtain a Lyapunov function but there many tricks to simplify the task.

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