Lagrange stability

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.

References

  • Elias P. Gyftopoulos, Lagrange Stability and Liapunov's Direct Method. Proc. of Symposium on Reactor Kinetics and Control, 1963. (PDF)
  • Bhatia, Nam Parshad; Szegő, Giorgio P. (2002). Stability theory of dynamical systems. Springer. ISBN 978-3-540-42748-3.


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