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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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A New Example on Lyapunov Stability [PDF]
Journal of Dynamics and Differential Equations, 2021 The purpose of this paper is to present an example of an Ordinary Differential Equation $x'=F(x)$ in the infinite-dimensional Hilbert space $\ell^2$ with $F$ being of class $\mathcal{C}^1$ in the Fréchet sense, such that the origin is an asymptotically stable equilibrium point but the spectrum of the linearized operator $DF(0)$ intersects the half ...
Hildebrando M. Rodrigues +1 more
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Feedback Stabilization and Lyapunov Functions [PDF]
SIAM Journal on Control and Optimization, 2000 The authors consider the problem of finding a feedback stabilizing law \(x \to k(x)\) associated with a control system \(x'(t) = f(x(t),u(t))\). Using the concept of positional strategies introduced in the framework of differential games by Krasovskii and Subbotin in 1988, assuming the existence of a Lyapunov Lipschitz function \(V\) defined on the ...
Francis H. Clarke +3 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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Lyapunov Functions for State Observers of Dynamic Systems Using Hamilton–Jacobi Inequalities
Mathematics, 2020 Lyapunov functions enable analyzing the stability of dynamic systems described by ordinary differential equations without finding the solution of such equations. For nonlinear systems, devising a Lyapunov function is not an easy task to solve in general.
Angelo Alessandri
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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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Optimal Stabilization Using Lyapunov Measures [PDF]
IEEE Transactions on Automatic Control, 2008 Numerical solutions for the optimal feedback stabilization of discrete time dynamical systems is the focus of this paper. Set-theoretic notion of almost everywhere stability introduced by the Lyapunov measure, weaker than conventional Lyapunov function-based stabilization methods, is used for optimal stabilization.
Arvind U. Raghunathan, Umesh Vaidya
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Nonlinear Analysis, 2022 This paper investigates practical stability for a class of fractional-order impulsive control coupled systems with noninstantaneous impulses on networks.
Jin You, Shurong Sun
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