Results 11 to 20 of about 7,527 (244)
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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Mathematics, 2023 In recent years, various qualitative investigations of the properties of differential equations with different types of generalizations of Riemann–Liouville fractional derivatives were studied and stability properties were investigated, usually using ...
Ravi P. Agarwal +2 more
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On perturbing lyapunov functions [PDF]
Mathematical Systems Theory, 1976 A new idea of perturbing Lyapunov functions is presented which permits one to discuss nonuniform properties of solutions of differential equations under weaker ...
V. Lakshmikantham, S. Leela
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An algorithm for constructing Lyapunov functions
Electronic Journal of Differential Equations, 2007 In this monograph we develop an algorithm for constructing Lyapunov functions for arbitrary switched dynamical systems $dot{mathbf{x}} = mathbf{f}_sigma(t,mathbf{x})$, possessing a uniformly asymptotically stable equilibrium.
Sigurdur Freyr Hafstein
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Eigenpairs for the Analysis of Complete Lyapunov Functions
Complexity, 2022 A complete Lyapunov function describes the qualitative behaviour of a dynamical system: the areas where the orbital derivative vanishes and where it is strictly negative characterise the chain recurrent set and the gradient-like flow, respectively ...
Carlos Argáez +2 more
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The Investigation of Nonlinear Polynomial Control Systems
Моделирование и анализ информационных систем, 2021 The paper considers methods for estimating stability using Lyapunov functions, which are used for nonlinear polynomial control systems. The apparatus of the Gro¨bner basis method is used to assess the stability of a dynamical system. A description of the
Sergei Nikolaevich Chukanov +1 more
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Finite-Time Lyapunov Functions and Impulsive Control Design
Complexity, 2020 In this paper, we introduce finite-time Lyapunov functions for impulsive systems. The relaxed sufficient conditions for asymptotic stability of an equilibrium of an impulsive system are given via finite-time Lyapunov functions.
Huijuan Li, Qingxia Ma
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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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Automatica, 2011 Abstract Lyapunov functions are a fundamental tool to investigate the stability properties of equilibrium points in linear or nonlinear systems. Unfortunately, even if the existence of Lyapunov functions for asymptotically stable equilibrium points is guaranteed by converse Lyapunov theorems, the actual computation of the analytic expression of the ...
Sassano M., Astolfi A.
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Feedback Stabilization and Lyapunov Functions [PDF]
SIAM Journal on Control and Optimization, 2000 Given a locally defined, nondifferentiable but Lipschitz Lyapunov function, we employ it in order to construct a (discontinuous) feedback law which stabilizes the underlying system to any given tolerance. A converse result shows that suitable Lyapunov functions of this type exist under mild assumptions.
Clarke, F.H. +3 more
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