On the stability of input-affine nonlinear systems with sampled-data control

Hassan Omran 1 Laurentiu Hetel 1 Jean-Pierre Richard 2, 1, 3 Françoise Lamnabhi-Lagarrigue 4
1 SyNeR - Systèmes Non Linéaires et à Retards
CRIStAL - Centre de Recherche en Informatique, Signal et Automatique de Lille (CRIStAL) - UMR 9189
3 NON-A - Non-Asymptotic estimation for online systems
Inria Lille - Nord Europe, CRIStAL - Centre de Recherche en Informatique, Signal et Automatique de Lille (CRIStAL) - UMR 9189
4 Division Systèmes - L2S
L2S - Laboratoire des signaux et systèmes : 1289
Abstract : This paper is dedicated to the stability analysis of nonlinear sampled-data systems, which are affine in the input. Assuming that a stabilizing continuous-time controller exists and it is implemented digitally, we intend to provide sufficient asymptotic/exponential stability conditions for the sampled-data system. This allows to find an estimate of the upper bound on the asynchronous sampling periods. The stability analysis problem is formulated both globally and locally. The main idea of the paper is to address the stability problem in the framework of dissipativity theory. Furthermore, the result is particularized for the class of polynomial input-affine sampled-data systems, where stability may be tested numerically using sum of squares decomposition and semidefinite programming.
Document type :
Conference papers
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https://hal-supelec.archives-ouvertes.fr/hal-00830881
Contributor : Françoise Lamnabhi-Lagarrigue <>
Submitted on : Wednesday, June 5, 2013 - 9:03:03 PM
Last modification on : Friday, March 22, 2019 - 1:36:01 AM

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  • HAL Id : hal-00830881, version 1

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Hassan Omran, Laurentiu Hetel, Jean-Pierre Richard, Françoise Lamnabhi-Lagarrigue. On the stability of input-affine nonlinear systems with sampled-data control. 12th European Control Conference (ECC 2013), Jul 2013, Zurich, Switzerland. pp.NC. ⟨hal-00830881⟩

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