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Article Dans Une Revue Automatica Année : 2023

Computational tractable guaranteed numerical method to study the stability of n-dimensional time-independent nonlinear systems with bounded perturbation

Méthode numérique garantie à complexité polynomiale, pour étudier la stabilité des systèmes non linéaires à n-dimensions indépendants du temps avec perturbations bornées

Résumé

The stability analysis of nonlinear continuous systems often requires manual calculation, which can become time-consuming when dealing with complex systems. Some works use positive invariant sets to discuss stability. These sets can be numerically approximated using Interval analysis but the computational complexity is exponential. In this paper, we propose a computational tractable numerical but guaranteed method based on Interval analysis to verify the robust positive invariance of ellipsoids to automatize the study of n-dimensional nonlinear systems' stability. This method relies on a fast enclosure of a state integration by an Euler method. Interval analysis guarantees the results of the developed algorithms. Several examples show the effectiveness of the proposed approaches on $n$-dimensional non-asymptotical continuous systems subject to bounded perturbation.
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Dates et versions

hal-04254326 , version 1 (23-10-2023)

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Morgan Louedec, Luc Jaulin, Christophe Viel. Computational tractable guaranteed numerical method to study the stability of n-dimensional time-independent nonlinear systems with bounded perturbation. Automatica, 2023, 153, pp.110981. ⟨10.1016/j.automatica.2023.110981⟩. ⟨hal-04254326⟩
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