Lyapunov stability theory
E181622
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.
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]
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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.
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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.
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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.
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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.
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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 stability theory
self-linksurface differs
ⓘ
surface form:
Lyapunov’s direct method
Lyapunov stability theory self-linksurface differs ⓘ
surface form:
Lyapunov’s indirect method
|
| 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 exponents ⓘ
surface form:
Lyapunov exponent
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
The pipeline generated the facts above by prompting gpt-5.1 with this entity's name + description and the instruction below.
Instruction
You are a knowledge base construction expert. Given a subject entity and a description of it, return factual statements that you know for the subject as a JSON list of dictionaries(triples), where keys must be "subject", "predicate" and "object". The number of facts may be very high, between 25 to 50 or more, for very popular subjects. For less popular subjects, the number of facts can be very low, like 5 or 10. # Requirements - If you don't know the subject at all, return an empty list. - If the subject is not a named entity, return an empty list. - Include at least one triple where predicate is "instanceOf". - Do not get too wordy. - Separate several objects into multiple triples with one object.
Input
Subject: Lyapunov stability theory Description of subject: 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.
Referenced by (14)
Full triples — surface form annotated when it differs from this entity's canonical label.
this entity surface form:
Lyapunov functions
this entity surface form:
Lyapunov stability
this entity surface form:
Lyapunov function
this entity surface form:
Lyapunov stability
this entity surface form:
Lyapunov stability
this entity surface form:
Lyapunov stability
this entity surface form:
Lyapunov’s direct method
this entity surface form:
Lyapunov’s indirect method
this entity surface form:
Lyapunov function
this entity surface form:
Lyapunov’s second method
this entity surface form:
Lyapunov stability