Paper Citation Record · LEDGER

A Converse Control Lyapunov Theorem for Joint Safety and Stability

As of 12 August 2026, this Paper Citation Record lists 31 of 31 outbound references and 0 inbound Pith citation observations for arXiv:2509.12182.

A citation records a reference. It does not transfer a finding from one paper to another.

pith.paper-citation-record.v1
2509.12182 v2

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measured 31 of 31 reference resolution

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Source: paper_references, paper_reference_links, observed 2026-08-04T16:45:04.942908Z

measured 31 of 31 standing notices

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Source: scholarly_work_events, retraction_status_cache, observed 2026-08-12T06:34:41.77262+00:00

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31 of 31 outbound references displayed

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Outbound references

Observation e9a1e87c-09b0-4044-b6b9-6e799e2fde50 · outbound

This paper cites Control barrier func- tions: Theory and applications.

A Converse Control Lyapunov Theorem for Joint Safety and Stability Control barrier func- tions: Theory and applications

Reference 1

Resolution: unresolved; no resolver link, observed 2026-08-04T16:45:02.827945Z

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Observation 4c5266ca-c5b4-465d-aaf7-d5c6bf95cd93 · outbound

This paper cites Control barrier function based quadratic programs for safety critical systems.IEEE Transactions on Automatic Control, 62(8):3861–3876, 2017.

A Converse Control Lyapunov Theorem for Joint Safety and Stability Control barrier function based quadratic programs for safety critical systems.IEEE Transactions on Automatic Control, 62(8):3861–3876, 2017

Reference 2

Resolution: unresolved; no resolver link, observed 2026-08-04T16:45:02.904452Z

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Observation fd8d24c7-0a88-4e1a-b5c5-d3ca99e5191b · outbound

This paper cites Stabilization with relaxed controls.Nonlinear Analysis: Theory, Methods & Applications, 7(11):1163–1173, 1983.

A Converse Control Lyapunov Theorem for Joint Safety and Stability Stabilization with relaxed controls.Nonlinear Analysis: Theory, Methods & Applications, 7(11):1163–1173, 1983

Reference 3

Resolution: unresolved; no resolver link, observed 2026-08-04T16:45:02.967091Z

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Observation 762266b0-17cd-436c-a186-5c9406153563 · outbound

This paper cites On (the existence of) control Lyapunov barrier functions.

A Converse Control Lyapunov Theorem for Joint Safety and Stability On (the existence of) control Lyapunov barrier functions

Reference 4

Resolution: unresolved; no resolver link, observed 2026-08-04T16:45:03.053563Z

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Observation 8fe642b2-7ef7-4784-95ba-ea6cafb2e22f · outbound

This paper cites stabilization with guaranteed safety using control Lyapunov–barrier function.

A Converse Control Lyapunov Theorem for Joint Safety and Stability stabilization with guaranteed safety using control Lyapunov–barrier function

Reference 5

Resolution: unresolved; no resolver link, observed 2026-08-04T16:45:03.142575Z

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Observation 8608c151-8113-4d98-882c-0d25f1da8838 · outbound

This paper cites Crowl and J.F.

A Converse Control Lyapunov Theorem for Joint Safety and Stability Crowl and J.F

Reference 6

Resolution: unresolved; no resolver link, observed 2026-08-04T16:45:03.211732Z

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Observation a6d663a2-ea39-4fc6-ba94-97d2d88f81e1 · outbound

This paper cites Verification and synthesis of compatible control lyapunov and control barrier functions.

A Converse Control Lyapunov Theorem for Joint Safety and Stability Verification and synthesis of compatible control lyapunov and control barrier functions

Reference 7

Resolution: unresolved; no resolver link, observed 2026-08-04T16:45:03.250041Z

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Observation 81243d0b-516a-4202-8c84-e92be04ac2f3 · outbound

This paper cites Safe nonlinear control using robust neural Lyapunov-barrier functions.

A Converse Control Lyapunov Theorem for Joint Safety and Stability Safe nonlinear control using robust neural Lyapunov-barrier functions

Reference 8

Resolution: unresolved; no resolver link, observed 2026-08-04T16:45:03.289634Z

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Observation 6feb8c7b-3038-4785-9467-f7e82ffa2754 · outbound

This paper cites Challenges in autonomous vehi- cle testing and validation.SAE International Journal of Transportation Safety, 4(1):15–24, 2016.

A Converse Control Lyapunov Theorem for Joint Safety and Stability Challenges in autonomous vehi- cle testing and validation.SAE International Journal of Transportation Safety, 4(1):15–24, 2016

Reference 9

Resolution: unresolved; no resolver link, observed 2026-08-04T16:45:03.340866Z

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Observation b45c10c4-69bc-4ff5-8b0f-5a6bf20bbbfc · outbound

This paper cites On the inversion of Lyapunov’s second theorem on stability of motion.Amer.

A Converse Control Lyapunov Theorem for Joint Safety and Stability On the inversion of Lyapunov’s second theorem on stability of motion.Amer

Reference 10

Resolution: unresolved; no resolver link, observed 2026-08-04T16:45:03.400381Z

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Observation 77351a45-1138-4d1b-8288-c825cab0cafb · outbound

This paper cites Lee.Introduction to Smooth Manifolds.

A Converse Control Lyapunov Theorem for Joint Safety and Stability Lee.Introduction to Smooth Manifolds

Reference 11

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Observation 73e201a4-543f-4450-87db-ceba3c0dcc09 · outbound

This paper cites an unresolved cited work.

A Converse Control Lyapunov Theorem for Joint Safety and Stability Unresolved cited work

Reference 12

Resolution: unresolved; no resolver link, observed 2026-08-04T16:45:03.574132Z

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Observation 19daedd7-9740-4f71-a42a-6ef685590c2f · outbound

This paper cites A graphical interpretation and universal formula for safe stabilization.

A Converse Control Lyapunov Theorem for Joint Safety and Stability A graphical interpretation and universal formula for safe stabilization

Reference 13

Resolution: unresolved; no resolver link, observed 2026-08-04T16:45:03.660831Z

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Observation 957ae118-f973-47cf-811d-62b462914569 · outbound

This paper cites A smooth converse Lyapunov theorem for robust stability.SIAM Journal on Control and Optimization, 34(1):124–160, 1996.

A Converse Control Lyapunov Theorem for Joint Safety and Stability A smooth converse Lyapunov theorem for robust stability.SIAM Journal on Control and Optimization, 34(1):124–160, 1996

Reference 14

Resolution: unresolved; no resolver link, observed 2026-08-04T16:45:03.749487Z

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Observation 95ba3739-734c-45ef-9396-2cac47588212 · outbound

This paper cites Physics-informed neural network Lyapunov functions: PDE charac- terization, learning, and verification.Automatica, 175:112193, 2025.

A Converse Control Lyapunov Theorem for Joint Safety and Stability Physics-informed neural network Lyapunov functions: PDE charac- terization, learning, and verification.Automatica, 175:112193, 2025

Reference 15

Resolution: unresolved; no resolver link, observed 2026-08-04T16:45:03.836273Z

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Observation e204c7e8-aaa0-45c6-bafd-51855d909c43 · outbound

This paper cites Smooth converse Lyapunov-barrier theorems for asymptotic stability with safety constraints and reach-avoid-stay specifications.Automatica, 144:110478, 2022.

A Converse Control Lyapunov Theorem for Joint Safety and Stability Smooth converse Lyapunov-barrier theorems for asymptotic stability with safety constraints and reach-avoid-stay specifications.Automatica, 144:110478, 2022

Reference 16

Resolution: unresolved; no resolver link, observed 2026-08-04T16:45:03.893376Z

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Observation 932004b0-5c8c-4990-a8e7-5dc7bcc9b0c3 · outbound

This paper cites Optimization-based safe stabilizing feedback with guaranteed region of attraction.IEEE Control Systems Letters, 7:367–372, 2022.

A Converse Control Lyapunov Theorem for Joint Safety and Stability Optimization-based safe stabilizing feedback with guaranteed region of attraction.IEEE Control Systems Letters, 7:367–372, 2022

Reference 17

Resolution: unresolved; no resolver link, observed 2026-08-04T16:45:03.962408Z

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Observation 4ef101e8-2095-49ef-b26e-16d3b363e28d · outbound

This paper cites Converse theorems for certificates of safety and stability, 2025.

A Converse Control Lyapunov Theorem for Joint Safety and Stability Converse theorems for certificates of safety and stability, 2025

Reference 18

Resolution: unresolved; no resolver link, observed 2026-08-04T16:45:04.023496Z

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Observation f4cc51ac-9d89-4204-8ede-31e21797369a · outbound

This paper cites ¨Uber die lage der integralkurven gew ¨ohnlicher differentialgleichungen.Proceedings of the Physico-Mathematical Society of Japan, 24:551–559, 1942.

A Converse Control Lyapunov Theorem for Joint Safety and Stability ¨Uber die lage der integralkurven gew ¨ohnlicher differentialgleichungen.Proceedings of the Physico-Mathematical Society of Japan, 24:551–559, 1942

Reference 19

Resolution: unresolved; no resolver link, observed 2026-08-04T16:45:04.089408Z

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Observation 4aea5fef-e8ce-46df-a51d-b37bf4763c4e · outbound

This paper cites Ong.Uniting and Balancing Control Objectives: Safety, Stability, Smoothness, and Resource Conservation.

A Converse Control Lyapunov Theorem for Joint Safety and Stability Ong.Uniting and Balancing Control Objectives: Safety, Stability, Smoothness, and Resource Conservation

Reference 20

Resolution: unresolved; no resolver link, observed 2026-08-04T16:45:04.161356Z

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Observation 1b561b7c-1bdf-480b-87a5-95a8975cfd05 · outbound

This paper cites Universal formula for smooth safe stabilization.

A Converse Control Lyapunov Theorem for Joint Safety and Stability Universal formula for smooth safe stabilization

Reference 21

Resolution: unresolved; no resolver link, observed 2026-08-04T16:45:04.268925Z

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Observation bea23df1-d31a-4e55-b5d3-d55fb8a11070 · outbound

This paper cites Stabiliza- tion with guaranteed safety using control Lyapunov–barrier function.

A Converse Control Lyapunov Theorem for Joint Safety and Stability Stabiliza- tion with guaranteed safety using control Lyapunov–barrier function

Reference 22

Resolution: unresolved; no resolver link, observed 2026-08-04T16:45:04.355357Z

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Observation 2858ca0d-91c3-4fb4-8412-e838b2f4548b · outbound

This paper cites A Lyapunov-like characterization of asymptotic controllability.SIAM journal on control and optimization, 21(3):462– 471, 1983.

A Converse Control Lyapunov Theorem for Joint Safety and Stability A Lyapunov-like characterization of asymptotic controllability.SIAM journal on control and optimization, 21(3):462– 471, 1983

Reference 23

Resolution: unresolved; no resolver link, observed 2026-08-04T16:45:04.411828Z

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Observation 61d5bb29-9876-4255-9328-e4a06046eb9d · outbound

This paper cites A ‘universal’construction of Artstein’s theorem on nonlinear stabilization.Systems & Control Letters, 13(2):117–123, 1989.

A Converse Control Lyapunov Theorem for Joint Safety and Stability A ‘universal’construction of Artstein’s theorem on nonlinear stabilization.Systems & Control Letters, 13(2):117–123, 1989

Reference 24

Resolution: unresolved; no resolver link, observed 2026-08-04T16:45:04.493916Z

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Observation 4ed0d45c-f38b-42e8-933d-b7fd0cd5d5a5 · outbound

This paper cites Springer Science & Business Media, 1998.

A Converse Control Lyapunov Theorem for Joint Safety and Stability Springer Science & Business Media, 1998

Reference 25

Resolution: unresolved; no resolver link, observed 2026-08-04T16:45:04.581873Z

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Observation fdff21cf-9809-4a8c-950f-f085636dc4b5 · outbound

This paper cites Stability and stabilization: discontinuities and the effect of disturbances.

A Converse Control Lyapunov Theorem for Joint Safety and Stability Stability and stabilization: discontinuities and the effect of disturbances

Reference 26

Resolution: unresolved; no resolver link, observed 2026-08-04T16:45:04.647536Z

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Observation 0e4bbd09-1d0e-4f22-be30-3a1f7b896de7 · outbound

This paper cites A smooth Lyapunov function from a class-KLestimate involving two positive semidefinite functions.

A Converse Control Lyapunov Theorem for Joint Safety and Stability A smooth Lyapunov function from a class-KLestimate involving two positive semidefinite functions

Reference 27

Resolution: unresolved; no resolver link, observed 2026-08-04T16:45:04.694881Z

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Observation 176c1d8a-22dc-4bc9-bba0-8b731759fa6d · outbound

This paper cites Constructive safety using control barrier functions.IFAC Proceedings Volumes, 40(12):462–467, 2007.

A Converse Control Lyapunov Theorem for Joint Safety and Stability Constructive safety using control barrier functions.IFAC Proceedings Volumes, 40(12):462–467, 2007

Reference 28

Resolution: unresolved; no resolver link, observed 2026-08-04T16:45:04.743008Z

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Observation 4a02225a-c7f8-495d-8614-508078cba582 · outbound

This paper cites Control Lyapunov-barrier function-based model predictive control of nonlinear systems.Au- tomatica, 109:108508, 2019.

A Converse Control Lyapunov Theorem for Joint Safety and Stability Control Lyapunov-barrier function-based model predictive control of nonlinear systems.Au- tomatica, 109:108508, 2019

Reference 29

Resolution: unresolved; no resolver link, observed 2026-08-04T16:45:04.808628Z

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Observation 83125699-3518-48fc-bc34-147e62ec9ea4 · outbound

This paper cites Constrained control of input–output linearizable systems using control sharing barrier functions.Automatica, 87:195–201, 2018.

A Converse Control Lyapunov Theorem for Joint Safety and Stability Constrained control of input–output linearizable systems using control sharing barrier functions.Automatica, 87:195–201, 2018

Reference 30

Resolution: unresolved; no resolver link, observed 2026-08-04T16:45:04.852303Z

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Observation 40c1ef1c-b3a8-4bcb-8ea1-59b991418ab5 · outbound

This paper cites Robustness of control barrier functions for safety critical control.

A Converse Control Lyapunov Theorem for Joint Safety and Stability Robustness of control barrier functions for safety critical control

Reference 31

Resolution: unresolved; no resolver link, observed 2026-08-04T16:45:04.942908Z

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