Aleksandr Lyapunov

Aleksandr Mikhailovich Lyapunov (1857–1918) was a Russian mathematician and engineer whose work established major methods for analyzing dynamical stability and contributed to probability theory.

Dynamical system: A system whose state changes over time according to specified rules. His stability theory asks how trajectories of such systems behave near a particular state.
Lyapunov stability: A property in which solutions starting sufficiently near an equilibrium remain near it for all later time. This is the central behavior his stability methods were designed to test.
Control theory: The study of how inputs can guide the behavior of dynamical systems. Lyapunov functions provide certificates that a feedback controller stabilizes a system.
Pafnuty Chebyshev: A Russian mathematician whose work shaped probability theory, number theory, and approximation. Chebyshev supervised Lyapunov’s studies and helped form the mathematical tradition in which he worked.
Kharkiv University: A Ukrainian university founded in Kharkiv in 1804, historically known as Imperial Kharkov University. Lyapunov studied there and began his mathematical career in the institution’s academic environment.
Equilibrium point: A state of a dynamical system that remains unchanged under its governing dynamics. Lyapunov stability is commonly tested by perturbing an equilibrium and tracking the resulting motion.
Lyapunov function: A scalar function whose change along system trajectories helps establish stability or instability. Its decrease along trajectories replaces the need to solve the differential equations explicitly.
Nonlinear control: Control theory for systems whose governing equations are nonlinear in their states or inputs. Lyapunov’s direct method is especially useful when nonlinear system solutions are difficult to calculate.
Andrey Markov: A Russian mathematician known for foundational work on stochastic processes and probability. Markov belonged to the same St. Petersburg mathematical school and developed probability after Lyapunov.
St. Petersburg University: A Russian university founded in 1724 and among the oldest institutions of higher education in the country. Lyapunov held an academic post there after moving from Kharkiv.

Linked from 2 pages

Stability theoryRelated: His 1892 work introduced the function-based approach that bears his name.