Lagrange stability is a concept in the stability theory of dynamical systems, named after Joseph-Louis Lagrange.
For any point in the state space,
in a real continuous dynamical system
is said to be positively Lagrange stable if the positive semi-orbit
is compact, then the motion is said to be negatively Lagrange stable.
is said to be Lagrange stable if it is both positively and negatively Lagrange stable.
If the state space
is the Euclidean space
, then the above definitions are equivalent to
A dynamical system is said to be positively-/negatively-/Lagrange stable if for each
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