Estimating the robust domain of attraction for non-smooth systems using an interval Lyapunov equation

Abstract : The Lyapunov equation allows finding a quadratic Lyapunov function for an asymptotically stable fixed point of a linear system. Applying this equation to the linearization of a nonlinear system can also prove the exponential stability of its fixed points. This paper proposes an interval version of the Lyapunov equation, which allows investigating a given Lyapunov candidate function for non-smooth nonlinear systems inside an explicitly given neighborhood, leading to rigorous estimates of the domain of attraction (EDA) of exponentially stable fixed points. These results are developed in the context of uncertain systems. Experiments are presented, which show the interest of the approach including with respect to usual approaches based on sum-of-squares for the computation of EDA.
Type de document :
Communication dans un congrès
The 18th International Symposium on Scientific Computing, Computer Arithmetic, and Verified Numerical Computations, Sep 2018, Tokyo, Japan
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https://hal.archives-ouvertes.fr/hal-02008057
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Soumis le : mardi 5 février 2019 - 15:12:29
Dernière modification le : mardi 19 février 2019 - 09:29:56

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GoldsztejnChabert-SCAN2018.pdf
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  • HAL Id : hal-02008057, version 1

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Alexandre Goldsztejn, Gilles Chabert. Estimating the robust domain of attraction for non-smooth systems using an interval Lyapunov equation. The 18th International Symposium on Scientific Computing, Computer Arithmetic, and Verified Numerical Computations, Sep 2018, Tokyo, Japan. 〈hal-02008057〉

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