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Lyapunov stability of the subgradient method with constant step size [PDF]
Mathematical programming, 2022 We consider the subgradient method with constant step size for minimizing locally Lipschitz semi-algebraic functions. In order to analyze the behavior of its iterates in the vicinity of a local minimum, we introduce a notion of discrete Lyapunov ...
C. Josz, Lexiao Lai
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Lyapunov stability tests for linear time-delay systems [PDF]
Annual Reviews in Control, 2022 An overview of stability conditions in terms of the Lyapunov matrix for time-delay systems is presented. The main results and proof are presented in details for the case of systems with multiple delays.
Sabine Mondi'e, A. Egorov, M. A. Gómez
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Direct data-driven model-reference control with Lyapunov stability guarantees [PDF]
IEEE Conference on Decision and Control, 2021 We introduce a novel data-driven model-reference control design approach for unknown linear systems with fully measurable state. The proposed control action is composed by a static feedback term and a reference tracking block shaped from data to ...
V. Breschi +3 more
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A Discussion on the Existence of Smooth Lyapunov Functions for Continuous Stable Systems [PDF]
International Journal of Industrial Electronics, Control and Optimization, 2021 Lyapunov's theorem is the basic criteria to establish the stability properties of the nonlinear dynamical systems. In this method, it is a necessity to find the positive definite functions with negative definite or negative semi-definite derivative ...
Majid Akbarian, Naser Pariz
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Stability of the Vallis System
Современные информационные технологии и IT-образование, 2022 In this paper, a variational method is proposed for obtaining the necessary (and sufficient) stability conditions for perturbed solutions of the system of Vallis equations.
Vladimir Nefedov +2 more
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Stability of the Lorentz System
Современные информационные технологии и IT-образование, 2021 In this paper, a variational method is proposed for obtaining the necessary (and sufficient) stability conditions for perturbed solutions of the system of Lorentz equations.
Vasiliy Tikhomirov +3 more
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Neural Lyapunov Control of Unknown Nonlinear Systems with Stability Guarantees [PDF]
Neural Information Processing Systems, 2022 Learning for control of dynamical systems with formal guarantees remains a challenging task. This paper proposes a learning framework to simultaneously stabilize an unknown nonlinear system with a neural controller and learn a neural Lyapunov function to
Rui Zhou +3 more
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A Lyapunov Function for Robust Stability of Moving Horizon Estimation [PDF]
IEEE Transactions on Automatic Control, 2022 We provide a novel robust stability analysis for moving horizon estimation (MHE) using a Lyapunov function. In addition, we introduce linear matrix inequalities (LMIs) to verify the necessary incremental input/output-to-state stability ($\boldsymbol ...
J. Schiller +4 more
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Lyapunov Stability in the Cournot Duopoly Game
Discrete Dynamics in Nature and Society, 2023 This paper studies Lyapunov stability at a point and its application in the Cournot duopoly game. We first explore the relationship between Lyapunov stability at a point, nonsensitivity and non-Devaney chaos and find that a dynamical system is ...
Dan Zhu, Debing Ni
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Control and Synchronization of a Novel Realizable Nonlinear Chaotic System
Fractal and Fractional, 2023 The study proposes a novel chaotic system with a cubic non-linear term. Different system characteristics are investigated including equilibria, stability, invariance, dissipation, Lyapunov dimension, and Lyapunov exponents.
Mohammed Almuzaini, Abdullah Alzahrani
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