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Continuous and discrete-time stability of a robust set-valued nested controller

Abstract : We propose a set-valued controller with a signum multifunction nested inside another one. We prove that the controller is well posed and achieves robust ultimate boundedness in the presence of mismatched, non-vanishing disturbances. Even more, the selected output can be made arbitrarily small. Also, by applying an implicit/explicit Euler scheme similar to the one introduced by Acary and Brogliato (2010) for matched disturbances, we derive a selection strategy for the discrete-time implementation of the set-valued control law. Simulations demonstrate that the discrete scheme diminishes chattering substantially, compared with a fully explicit method.
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https://hal.inria.fr/hal-01944920
Contributor : Bernard Brogliato <>
Submitted on : Wednesday, June 26, 2019 - 8:05:04 AM
Last modification on : Tuesday, May 11, 2021 - 11:36:30 AM

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Felix Miranda-Villatoro, Fernando Castaños, Bernard Brogliato. Continuous and discrete-time stability of a robust set-valued nested controller. Automatica, Elsevier, 2019, 107, pp.406-417. ⟨10.1016/j.automatica.2019.06.003⟩. ⟨hal-01944920v2⟩

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