Lyapunov stability [SEP] named after
the thesis "The General Problem of Stability of Motion" at Kharkov University in 1892. A. M. Lyapunov was a pioneer in successful endeavoring to develop the global approach to the analysis of the stability of nonlinear dynamical systems by comparison with the widely spread local method of linearizing them about points of equilibrium. His work, initially published in Russian and then translated to French, received little attention for many years. The mathematical theory of stability of motion, founded by A. M. Lyapunov, considerably anticipated the time for its implementation in science
is asymptotically stable. The notion of exponential stability guarantees a minimal rate of decay, i.e., an estimate of how quickly the solutions converge. The idea of Lyapunov stability can be extended to infinite-dimensional manifolds, where it is known as structural stability, which concerns the behavior of different but "nearby" solutions to differential equations. Input-to-state stability (ISS) applies Lyapunov notions to systems with inputs.
History.
Lyapunov stability is named after  Aleksandr Mikhailovich Lyapunov, a Russian mathematician who defended