LaSalle’s invariance principle
E695937
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.
All labels observed (1)
| Label | Occurrences |
|---|---|
| LaSalle’s invariance principle canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T7833119 — 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: LaSalle’s invariance principle Context triple: [Lyapunov stability theory, relatedTo, LaSalle’s invariance principle]
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A.
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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B.
Inners and Stability of Dynamic Systems
"Inners and Stability of Dynamic Systems" is a seminal work in control theory by Eliahu I. Jury that analyzes the role of inner functions in determining the stability properties of dynamic systems.
-
C.
Stability of Linear Systems
"Stability of Linear Systems" is a foundational book by Eliahu I. Jury that systematically develops the theory and criteria for determining the stability of linear dynamical and control systems.
-
D.
Hamilton’s maximum principle
Hamilton’s maximum principle is a fundamental analytical tool in geometric analysis that extends the classical maximum principle to tensor-valued quantities, playing a key role in studying the behavior of solutions to the Ricci flow and related geometric evolution equations.
-
E.
Freidlin–Wentzell theory
Freidlin–Wentzell theory is a mathematical framework in probability that analyzes the behavior of stochastic dynamical systems under small random perturbations using large deviation principles.
- 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: LaSalle’s invariance principle Target entity description: 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.
-
A.
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.
-
B.
Inners and Stability of Dynamic Systems
"Inners and Stability of Dynamic Systems" is a seminal work in control theory by Eliahu I. Jury that analyzes the role of inner functions in determining the stability properties of dynamic systems.
-
C.
Stability of Linear Systems
"Stability of Linear Systems" is a foundational book by Eliahu I. Jury that systematically develops the theory and criteria for determining the stability of linear dynamical and control systems.
-
D.
Hamilton’s maximum principle
Hamilton’s maximum principle is a fundamental analytical tool in geometric analysis that extends the classical maximum principle to tensor-valued quantities, playing a key role in studying the behavior of solutions to the Ricci flow and related geometric evolution equations.
-
E.
Freidlin–Wentzell theory
Freidlin–Wentzell theory is a mathematical framework in probability that analyzes the behavior of stochastic dynamical systems under small random perturbations using large deviation principles.
- F. None of above. chosen
Statements (48)
| Predicate | Object |
|---|---|
| instanceOf |
mathematical theorem
ⓘ
result in dynamical systems theory ⓘ |
| appliedIn |
biological systems modeling
ⓘ
engineering ⓘ mechanical systems ⓘ power systems stability ⓘ robotics ⓘ |
| appliesTo |
autonomous dynamical systems
ⓘ
continuous-time systems ⓘ nonlinear differential equations ⓘ ordinary differential equations ⓘ |
| assumes |
existence of a Lyapunov function with nonpositive derivative
ⓘ
forward completeness of solutions on the considered set ⓘ |
| characterizes |
asymptotic stability
ⓘ
limit behavior of trajectories ⓘ |
| concerns |
invariance of sets under system flow
ⓘ
long-term behavior of solutions ⓘ |
| concludes |
solutions converge to invariant sets where Lyapunov derivative vanishes
ⓘ
trajectories approach the largest invariant set in the region ⓘ |
| conditionOn |
existence of largest invariant set where Lyapunov derivative is zero
ⓘ
negative semidefinite derivative of Lyapunov function ⓘ nonincreasing Lyapunov function along trajectories ⓘ |
| field |
control theory
ⓘ
dynamical systems ⓘ nonlinear systems ⓘ stability theory ⓘ |
| generalizes | Lyapunov’s direct method NERFINISHED ⓘ |
| hasVariant |
LaSalle–Yoshizawa theorem
NERFINISHED
ⓘ
discrete-time LaSalle invariance principle ⓘ |
| implies |
asymptotic stability of equilibrium under suitable conditions
ⓘ
convergence to equilibrium when the largest invariant set is an equilibrium ⓘ |
| namedAfter | Joseph P. LaSalle NERFINISHED ⓘ |
| relatedTo |
Barbashin–Krasovskii theorem
NERFINISHED
ⓘ
Lyapunov stability theory NERFINISHED ⓘ invariant set theorems ⓘ |
| timeDomain | time-continuous dynamics ⓘ |
| typicalAssumptionOnSet |
compact positively invariant set
ⓘ
trajectories remain in a bounded region ⓘ |
| usedFor |
analysis of limit sets
ⓘ
convergence analysis in adaptive control ⓘ convergence analysis in observer design ⓘ global asymptotic stability proofs ⓘ proving asymptotic stability without strict Lyapunov decrease ⓘ stability analysis of nonlinear control systems ⓘ |
| usesConcept |
Lyapunov function
NERFINISHED
ⓘ
asymptotic behavior of trajectories ⓘ invariant set ⓘ omega-limit set ⓘ |
How these facts were elicited
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Instruction
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Input
Subject: LaSalle’s invariance principle Description of subject: 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.
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.