Lyapunov function
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There are a family of function 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 founding 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 simplifly the task.
(stub, please complete)