Skip to Main content Skip to Navigation
Conference papers

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.
Complete list of metadatas

Cited literature [3 references]  Display  Hide  Download

https://hal.archives-ouvertes.fr/hal-02008057
Contributor : Ogre Equipe <>
Submitted on : Tuesday, February 5, 2019 - 3:12:29 PM
Last modification on : Wednesday, June 24, 2020 - 4:19:52 PM
Document(s) archivé(s) le : Monday, May 6, 2019 - 3:28:43 PM

File

GoldsztejnChabert-SCAN2018.pdf
Files produced by the author(s)

Identifiers

  • HAL Id : hal-02008057, version 1

Citation

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⟩

Share

Metrics

Record views

125

Files downloads

170