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Stabilization by a relay control using non-quadratic Lyapunov functions

Abstract : In this article we consider the stabilization problem by a relay control using non-quadratic Lyapunov functions. First, a general result is proposed for the case of nonlinear systems. A full state relay feedback controller is designed in order to ensure the local asymptotic stability of the closed-loop system. Then, the result is applied to the particular case of LTI systems. A constructive method based on LMI conditions is given in order to design nonlinear switching surfaces and provide an estimation of a non-ellipsoidal domain of attraction. In addition, the approach is extended to observer-based relay feedback. Both linear and nonlinear switching surfaces dependent on the estimated state are designed while using a Luenberger observer. Finally, illustrative examples are proposed in order to show the efficiency of the proposed methods and simulations are performed for a Buck converter structure.
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https://hal.inria.fr/hal-01871693
Contributor : Christophe Fiter <>
Submitted on : Tuesday, September 11, 2018 - 10:48:35 AM
Last modification on : Friday, December 11, 2020 - 6:44:07 PM
Long-term archiving on: : Wednesday, December 12, 2018 - 1:31:01 PM

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Zohra Kader, Christophe Fiter, Laurentiu Hetel, Lotfi Belkoura. Stabilization by a relay control using non-quadratic Lyapunov functions. Automatica, Elsevier, 2018, 97, pp.353 - 366. ⟨10.1016/j.automatica.2018.08.020⟩. ⟨hal-01871693⟩

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