Lagrange stability
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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
, where
is
, the motion
is said to be positively Lagrange stable if the positive semi-orbit
is compact. If the negative semi-orbit
is compact, then the motion is said to be negatively Lagrange stable. The motion through
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
and
being bounded, respectively.
A dynamical system is said to be positively-/negatively-/Lagrange stable if for each , the motion
is positively-/negatively-/Lagrange stable, respectively.