Lagrange stability is a concept in the stability theory of dynamical systems, named after Joseph-Louis Lagrange.
For any point in the state space, x ∈ M in a real continuous dynamical system ( T , M , Φ ) , where T is R , the motion Φ ( t , x ) is said to be positively Lagrange stable if the positive semi-orbit γ x + is compact. If the negative semi-orbit γ x − is compact, then the motion is said to be negatively Lagrange stable. The motion through x is said to be Lagrange stable if it is both positively and negatively Lagrange stable. If the state space M is the Euclidean space R n , then the above definitions are equivalent to γ x + , γ x − and γ x being bounded, respectively.
A dynamical system is said to be positively-/negatively-/Lagrange stable if for each x ∈ M , the motion Φ ( t , x ) is positively-/negativey-/Lagrange stable, respectively.
