Lyapunov stability theory

A theory of the stability of motion, constructed by A.M. Lyapunov at the turn into 20th century (see [1]). At the basis of it lie the concepts of Lyapunov stability and asymptotic stability (see Asymptotically-stable solution), introduced by Lyapunov, Lyapunov's theorem on stability in the first approximation (on which Lyapunov's first method for investigating stability is based) and Lyapunov's second method (see Lyapunov function). The results and methods of Lyapunov, developed for the construction of stability theory, found important and numerous applications in mathematics, mechanics and engineering. See also Stability theory.

References

[1]	A.M. Lyapunov, "Stability of motion" , Acad. Press (1966) (Translated from Russian)