passivity theorem
E714450
The passivity theorem is a fundamental result in control theory that guarantees the stability of interconnected systems by analyzing their energy-dissipating (passive) properties.
All labels observed (1)
| Label | Occurrences |
|---|---|
| passivity theorem canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T8119364 — 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: passivity theorem Context triple: [small-gain theorem, relatedTo, passivity theorem]
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A.
small-gain theorem
The small-gain theorem is a fundamental result in control theory that provides a sufficient condition for the stability of feedback interconnections by requiring the product of system gains to be less than one.
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B.
Lyapunov 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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C.
Routh–Hurwitz stability criterion
The Routh–Hurwitz stability criterion is a mathematical test in control theory that determines whether all roots of a system’s characteristic polynomial lie in the left half of the complex plane, ensuring system stability without explicitly computing the roots.
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D.
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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E.
LaSalle’s invariance principle
LaSalle’s invariance principle is a fundamental result in dynamical systems theory that extends Lyapunov’s direct method by characterizing the asymptotic behavior of trajectories through invariant sets where a Lyapunov function’s derivative vanishes.
- 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: passivity theorem Target entity description: The passivity theorem is a fundamental result in control theory that guarantees the stability of interconnected systems by analyzing their energy-dissipating (passive) properties.
-
A.
small-gain theorem
The small-gain theorem is a fundamental result in control theory that provides a sufficient condition for the stability of feedback interconnections by requiring the product of system gains to be less than one.
-
B.
Lyapunov 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.
-
C.
Routh–Hurwitz stability criterion
The Routh–Hurwitz stability criterion is a mathematical test in control theory that determines whether all roots of a system’s characteristic polynomial lie in the left half of the complex plane, ensuring system stability without explicitly computing the roots.
-
D.
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.
-
E.
LaSalle’s invariance principle
LaSalle’s invariance principle is a fundamental result in dynamical systems theory that extends Lyapunov’s direct method by characterizing the asymptotic behavior of trajectories through invariant sets where a Lyapunov function’s derivative vanishes.
- F. None of above. chosen
Statements (49)
| Predicate | Object |
|---|---|
| instanceOf | theorem in control theory ⓘ |
| appliesTo |
Lur’e systems
ⓘ
feedback systems ⓘ interconnected systems ⓘ multiport networks ⓘ nonlinear systems ⓘ time-invariant systems ⓘ time-varying systems ⓘ |
| assumes |
causal systems
ⓘ
finite energy signals ⓘ |
| basedOn |
dissipation inequality
ⓘ
energy balance ⓘ storage functions ⓘ |
| condition |
each subsystem is passive
ⓘ
interconnection is power-conserving ⓘ well-posed feedback interconnection ⓘ |
| field |
control theory
ⓘ
network theory ⓘ systems theory ⓘ |
| formalizedBy |
storage function inequality
ⓘ
supply rate ⓘ |
| guarantees |
L2-stability for passive interconnections
ⓘ
input-output stability under passivity conditions ⓘ stability of interconnected passive systems ⓘ |
| hasKeyConcept |
Lyapunov stability
ⓘ
linked to:
Lyapunov stability theory
energy dissipation ⓘ feedback interconnection ⓘ input-output stability ⓘ passivity ⓘ stability ⓘ |
| hasVariant |
incremental passivity theorem
ⓘ
input strict passivity theorem ⓘ output strict passivity theorem ⓘ strict passivity theorem ⓘ |
| implies |
internal stability under certain detectability conditions
ⓘ
robustness to certain modeling uncertainties ⓘ |
| relatedTo |
Lyapunov’s direct method
ⓘ
linked to:
Lyapunov stability theory
bounded real lemma ⓘ dissipativity theory ⓘ positive real lemma ⓘ small-gain theorem ⓘ |
| usedIn |
aerospace control systems
ⓘ
biological systems modeling ⓘ haptics ⓘ mechanical systems control ⓘ networked control systems ⓘ power electronics control ⓘ robot control ⓘ teleoperation systems ⓘ |
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: passivity theorem Description of subject: The passivity theorem is a fundamental result in control theory that guarantees the stability of interconnected systems by analyzing their energy-dissipating (passive) properties.
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.