Lyapunov Stability

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Overview

Lyapunov stability asks whether a system’s behavior stays bounded near an equilibrium or converges toward it, a central concern in control, learning, and physical modeling. Researchers construct Lyapunov functions and use tools such as linear matrix inequalities, integral quadratic constraints, and Foster–Lyapunov drift conditions to certify stability in deterministic, stochastic, and learned systems. Neural networks, reinforcement-learning controllers, optimization algorithms, and sampling-based controllers are increasingly designed or analyzed with these certificates, often alongside benchmarks in robotics and nonlinear control. A key challenge is balancing guarantees that are rigorous and computable with ones that are not overly conservative, especially when stability is only local, noise or approximation errors persist, or systems have multiple attractors.

Latest papers

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23 papers2 papers in the last four weeks, down 33% on the four weeks before. 0.0% of all new papers.

  1. Length-Independent Stability and L2L_2-Gain Certificates for Chains of Delayed Neural Modules

    Oct 18, 2026Ömer Faruk İşcanlıNeural Network StabilityModular Neural Networks

    Department of Computer Engineering, Istanbul University-Cerrahpaşa, Istanbul, Türkiye

  2. Port-Hamiltonian Neural Networks for Systems with Multiple Asymptotically Stable Equilibria

    Oct 1, 2026Simon Heilig, Jens Püttschneider, Mohammad Itani +2Dynamical SystemsLyapunov Stability

    Faculty of Computer Science, Ruhr University Bochum, Germany · Institute of Control Systems, Hamburg University of Technology, Germany

  3. Neural ODEs Meet Concurrent Learning: Stable Online Learning with Lyapunov Guarantees

    Sep 26, 2026Omkar Sudhir PatilNeural ODEsNeural Network Training Dynamics

    Division of Electrical and Computer Engineering Louisiana State University Baton Rouge, LA 70803, USA

  4. Learning Provable Neural Network Observer for Uncertain Dynamical Systems

    Sep 25, 2026Zhangyi Wang, Jiaxu Liu, Song Chen +2Neural Network StabilityLyapunov Stability

    College of Control Science and Engineering, Zhejiang University, China · School of Science, Huzhou Normal University, China · Department of Mathematics, National University of Singapore, Singapore

  5. Learning Lyapunov Operators for Nonlinear Systems

    Sep 16, 2026Amartya Mukherjee, Maxwell Fitzsimmons, David C. Del Rey Fernández +1Dynamical SystemsLyapunov Stability

    Department of Applied Mathematics, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1

  6. Reflected UAS: Corrected Deterministic Stability and Direct CTMC Drift Calculation

    Jul 30, 2026Krishna SubediDynamical SystemsLyapunov Stability

    Neryva

  7. Beyond the Edge of Chaos: Stability-Expressivity Transfer in Reservoir Forecasting

    Jul 20, 2026Yao Du, Xingang WangLyapunov StabilityReservoir Computing

    School of Physics and Information Technology, Shaanxi Normal University, Xi’an 710062, China

  8. Adaptive MPPI with Online Disturbance Covariance Estimation: Provable Stability Tightening via Spatial Smoothing

    Jul 9, 2026Hyung-Jin Yoon, Hunmin KimLyapunov StabilityStochastic Approximation

    Department of Mechanical and Nuclear Engineering, Tennessee Technological University, Cookeville, TN, USA

  9. Finite-Sample Closed-Loop Stability of Model Predictive Path Integral Control for Linear Time-Invariant Systems

    Jul 4, 2026Hyung-Jin Yoon, Hunmin KimDynamical SystemsStochastic Linear Dynamical Systems

    Department of Mechanical and Nuclear Engineering, Tennessee Technological University, Cookeville, TN, USA

  10. Reachability Guarantees for Cart-Pole Swing-Up and Stabilization

    Jun 26, 2026Mohamed Khalid M JaffarReachability AnalysisLyapunov-Based Control

    Department of Aerospace Engineering University of Maryland, College Park, USA

  11. Feedback-Coupled Memory Systems in Continuous Time

    Jun 24, 2026Stefano GrassiDynamical SystemsMulti-Agent Coordination

    Bangkok University, Phahonyothin Rd, Khlong Nueng, Khlong Luang District, Pathum Thani 12120, Thailand

  12. Between Amnesia and Chaos: A Memory Stability Expressivity Trilemma for Trainable Dissipative Oscillator Networks

    Jun 7, 2026Caleb MunigetyDynamical SystemsLyapunov Stability

    Independent Researcher

  13. Let the Dynamics Flow: Stable Flow Matching Dynamical Systems

    Jun 2, 2026Rodrigo Pérez-Dattari, Francisco Leiva, Andrea Testa +3Flow MatchingLyapunov Stability

    Department of Robotics, Perception, and Learning, KTH Royal Institute of Technology, Stockholm, Sweden. · Advanced Mining Technology Center (AMTC) and Department of Electrical Engineering, Universidad de Chile, Santiago, Chile. · Bosch Center for Artificial Intelligence, Renningen, Germany. +1

  14. Non-Asymptotic Convergence of Stochastic Iterative Algorithms: A Lyapunov Framework

    May 29, 2026Zaiwei Chen, Siva Theja MaguluriControl Lyapunov FunctionsLyapunov Stability

    Purdue IE · Georgia Tech IE

  15. Sharp Spectral Thresholds for Logit Fixed Points

    May 15, 2026Tongxi WangDynamical SystemsLyapunov Stability

    Southeast University Nanjing, China

  16. A Unified Lyapunov-IQC Framework for Uniform Stability of Smooth Quadratic First-Order Accelerated Optimizers

    May 8, 2026Don Li, Dacian DaescuLyapunov StabilityAlgorithmic Stability

    Department of Mathematics & Statistics, Portland State University, Portland, OR 97201, USA

  17. Stability of Control Lyapunov Function Guided Reinforcement Learning

    May 3, 2026Zachary Olkin, William D. Compton, Aaron D. AmesRL ControlLyapunov Stability

    The authors are with the Department of Control and Dynamical Systems at the California Institute of Technology.

  18. State-Dependent Lyapunov Analysis of Rank-1 Matrix Factorization

    Apr 28, 2026Jaehong MoonEdge of StabilityLyapunov Stability

    Industrial & Enterprise Systems Engineering University of Illinois at Urbana-Champaign Urbana, IL 61801

  19. Stability Principle Underlying Passive Dynamic Walking of Rimless Wheel

    Apr 15, 2026Fumihiko AsanoRobot LocomotionLyapunov Stability

    School of Information Science, Japan Advanced Institute of Science and Technology, 1-1 Asahidai, Nomi, Ishikawa 923-1292, Japan

  20. Hybrid Energy-Based Models for Physical AI: Provably Stable Identification of Port-Hamiltonian Dynamics

    Mar 31, 2026Simone Betteti, Luca LaurentiEnergy-Based ModelsDynamical Systems

    RIAS Lab, The Italian Institute of Artificial Intelligence for Industry, Turin, 10129, IT · Delft Center for Systems and Control, TU Delft, Delft, 2600 AA, The Netherlands

  21. Verifiable Error Bounds for Physics-Informed Neural Network Solutions of Lyapunov and Hamilton-Jacobi-Bellman Equations

    Mar 20, 2026Jun LiuHJB EquationsNeural PDE Solvers

    Department of Applied Mathematics, Faculty of Mathematics, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada

  22. Lyapunov Stable Graph Neural Flow

    Mar 13, 2026Haoyu Chu, Xiaotong Chen, Wei Zhou +4Graph Neural NetworksAdversarial Robustness

    School of Computer Science and Technology / School of Artificial Intelligence, China University of Mining and Technology, Xuzhou 221008, China · School of Information Science and Technology, University of Science and Technology of China, Hefei 230026, China

  23. Local exponential stability of mean-field Langevin descent-ascent and associated particle system

    Feb 2, 2026Geuntaek Seo, Minseop Shin, Pierre Monmarché +1Nash EquilibriumLyapunov Stability