Stabilization by a relay control using non-quadratic Lyapunov functions
| Autor: | Christophe Fiter, Laurentiu Hetel, Lotfi Belkoura, Zohra Kader |
|---|---|
| Přispěvatelé: | Centre de Recherche en Informatique, Signal et Automatique de Lille - UMR 9189 (CRIStAL), Centrale Lille-Université de Lille-Centre National de la Recherche Scientifique (CNRS), Non-Asymptotic estimation for online systems (NON-A-POST), Inria Lille - Nord Europe, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Systèmes Non Linéaires et à Retards (SyNeR), Centrale Lille-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Centrale Lille-Université de Lille-Centre National de la Recherche Scientifique (CNRS) |
| Jazyk: | angličtina |
| Rok vydání: | 2018 |
| Předmět: |
Lyapunov function
0209 industrial biotechnology Observer (quantum physics) Computer science 02 engineering and technology law.invention nonlinear switching surfaces symbols.namesake 020901 industrial engineering & automation switched affine systems Exponential stability Control theory Relay law [INFO.INFO-AU]Computer Science [cs]/Automatic Control Engineering 0202 electrical engineering electronic engineering information engineering relay control State observer Electrical and Electronic Engineering Buck converter State (functional analysis) Nonlinear system local asymptotic stabilization Control and Systems Engineering linear time invariant systems symbols 020201 artificial intelligence & image processing |
| Zdroj: | Automatica Automatica, 2018, 97, pp.353-366. ⟨10.1016/j.automatica.2018.08.020⟩ Automatica, Elsevier, 2018, 97, pp.353-366. ⟨10.1016/j.automatica.2018.08.020⟩ |
| ISSN: | 0005-1098 |
| DOI: | 10.1016/j.automatica.2018.08.020⟩ |
| Popis: | International audience; 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. |
| Databáze: | OpenAIRE |
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