Lyapunov stability theory

E181622

concept in control theory concept in dynamical systems mathematical theory stability theory

Lyapunov stability theory is a fundamental framework in dynamical systems and control theory that uses energy-like functions to assess the stability of equilibrium points without explicitly solving differential equations.

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All labels observed (7)

Label	Occurrences
Lyapunov stability	5
Lyapunov stability theory canonical	3
Lyapunov function	2
Lyapunov functions	1
Lyapunov’s direct method	1
Lyapunov’s indirect method	1
Lyapunov’s second method	1

How this entity was disambiguated

This entity first appeared as the object of triple T1597807 — resolving that mention is where its identity was fixed. The disambiguator weighed these candidate entities and picked the highlighted one (or “None”, minting a new entity). This is how homonymy is resolved: the same surface form can point to different entities.

NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07

Target entity: Lyapunov stability theory
Context triple: [Aleksandr Lyapunov, notableWork, Lyapunov stability theory]

A. Nyquist stability criterion
The Nyquist stability criterion is a graphical frequency-domain method in control theory used to determine the stability of feedback systems by analyzing how their open-loop transfer function encircles a critical point in the complex plane.
B. Ulam stability
Ulam stability is a concept in the theory of functional equations that studies when approximate solutions imply the existence of exact solutions nearby, forming the basis of what is now called Hyers–Ulam stability.
C. Dynamic Systems and Control Division
The Dynamic Systems and Control Division is a technical division of the American Society of Mechanical Engineers focused on the modeling, analysis, and control of dynamic engineering systems.
D. control theory
Control theory is a branch of engineering and mathematics that studies how to model, analyze, and design systems that regulate their own behavior using feedback.
E. Poincaré–Bendixson theorem
The Poincaré–Bendixson theorem is a fundamental result in the qualitative theory of dynamical systems that characterizes the possible long-term behaviors of trajectories in two-dimensional continuous flows, ruling out chaotic dynamics in the plane.
F. None of above. chosen
G. Unsure - the case is ambiguous/there is not enough information to decide.

NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07

Target entity: Lyapunov stability theory
Target entity description: Lyapunov stability theory is a fundamental framework in dynamical systems and control theory that uses energy-like functions to assess the stability of equilibrium points without explicitly solving differential equations.

A. Nyquist stability criterion
The Nyquist stability criterion is a graphical frequency-domain method in control theory used to determine the stability of feedback systems by analyzing how their open-loop transfer function encircles a critical point in the complex plane.
B. Ulam stability
Ulam stability is a concept in the theory of functional equations that studies when approximate solutions imply the existence of exact solutions nearby, forming the basis of what is now called Hyers–Ulam stability.
C. Dynamic Systems and Control Division
The Dynamic Systems and Control Division is a technical division of the American Society of Mechanical Engineers focused on the modeling, analysis, and control of dynamic engineering systems.
D. control theory
Control theory is a branch of engineering and mathematics that studies how to model, analyze, and design systems that regulate their own behavior using feedback.
E. Poincaré–Bendixson theorem
The Poincaré–Bendixson theorem is a fundamental result in the qualitative theory of dynamical systems that characterizes the possible long-term behaviors of trajectories in two-dimensional continuous flows, ruling out chaotic dynamics in the plane.
F. None of above. chosen

Statements (50)

Predicate	Object
instanceOf	concept in control theory ⓘ concept in dynamical systems ⓘ mathematical theory ⓘ stability theory ⓘ
appliesTo	autonomous systems ⓘ continuous-time systems ⓘ discrete-time systems ⓘ linear systems ⓘ non-autonomous systems ⓘ nonlinear systems ⓘ ordinary differential equations ⓘ
basedOn	Lyapunov’s direct method ⓘ linked to: Lyapunov stability theory Lyapunov’s indirect method ⓘ linked to: Lyapunov stability theory
characterizes	robustness properties of systems ⓘ stability of dynamical systems ⓘ stability of equilibrium points ⓘ
developedBy	Aleksandr Lyapunov ⓘ
doesNotRequire	explicit solution of differential equations ⓘ
field	applied mathematics ⓘ control theory ⓘ dynamical systems ⓘ nonlinear systems ⓘ
historicalPeriod	late 19th century ⓘ
namedAfter	Aleksandr Lyapunov ⓘ
provides	conditions for asymptotic stability ⓘ conditions for exponential stability ⓘ conditions for input-to-state stability ⓘ conditions for uniform stability ⓘ sufficient conditions for stability ⓘ
relatedTo	LaSalle’s invariance principle ⓘ Lyapunov candidate function ⓘ Lyapunov equation ⓘ Lyapunov exponent ⓘ linked to: Lyapunov exponents Lyapunov inequality ⓘ
usedIn	adaptive control ⓘ feedback control design ⓘ model predictive control analysis ⓘ nonlinear control ⓘ observer design ⓘ robust control ⓘ sliding mode control ⓘ state estimation stability analysis ⓘ
usesConcept	Lyapunov function ⓘ asymptotic stability ⓘ energy-like function ⓘ equilibrium point ⓘ global stability ⓘ invariant set ⓘ local stability ⓘ stability ⓘ

How these facts were elicited