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Lyapunov Stability Analysis of a Mass-Spring system subject to Friction

Abstract : This paper deals with the stability analysis of a mass-spring system subject to friction using Lyapunov-based arguments. As the described system presents a stick-slip phenomenon, the mass may then periodically stick to the ground. The objective consists in developing numerically tractable conditions ensuring the global asymptotic stability of the unique equilibrium point. The approach proposed merges two intermediate results: The first one relies on the characterization of an attractor around the origin, in which converge the closed-loop trajectories. The second result assesses the regional asymptotic stability of the equilibrium point by estimating its basin of attraction. The main result relies on conditions allowing to ensure that the attractor issued from the first result is included in the basin of attraction of the origin computed form the second result. An illustrative example draws the interest of the approach.
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Submitted on : Monday, June 29, 2020 - 11:11:38 AM
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Matthieu Barreau, Sophie Tarbouriech, Frédéric Gouaisbaut. Lyapunov Stability Analysis of a Mass-Spring system subject to Friction. Systems and Control Letters, Elsevier, 2021, 150, pp.104910. ⟨10.1016/j.sysconle.2021.104910⟩. ⟨hal-02883529⟩



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