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About Lyapunov function
In the theory of ordinary differential equations (ODEs), Lyapunov functions, named after Aleksandr Lyapunov, are scalar functions that may be used to prove the stability of an equilibrium of an ODE. Lyapunov functions are important to stability theory of dynamical systems and control theory. A similar concept appears in the theory of general state-space Markov chains usually under the name Foster–Lyapunov functions.
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