Stability analysis of some classes of input-affine nonlinear systems with aperiodic sampled-data control

Hassan Omran 1 Laurentiu Hetel 2 Mihaly Petreczky 1 Jean-Pierre Richard 2, 3 Francoise Lamnabhi-Lagarrigue 4
1 Mines Douai EMD - École des Mines de Douai
2 CRIStAL - Centre de Recherche en Informatique, Signal et Automatique de Lille (CRIStAL) - UMR 9189
3 NON-A - Non-Asymptotic estimation for online systems
CRIStAL - Centre de Recherche en Informatique, Signal et Automatique de Lille (CRIStAL) - UMR 9189, Inria Lille - Nord Europe
4 L2S - Laboratoire des signaux et systèmes
Abstract : In this paper we investigate the stability analysis of nonlinear sampled-data systems, which are affine in the input. We assume that a stabilizing controller is designed using the emulation technique. We intend to provide sufficient stability conditions for the resulting sampled-data system. This allows to find an estimate of the upper bound on the asynchronous sampling intervals, for which stability is ensured. The main idea of the paper is to address the stability problem in a new framework inspired by the dissipativity theory. Furthermore, the result is shown to be constructive. Numerically tractable criteria are derived using linear matrix inequality for polytopic systems and using sum of squares technique for the class of polynomial systems.
Keywords : stability analysis sampled-data systems aperiodic sampling Nonlinear systems emulation approach
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TDS-MACS | INSTITUT-TELECOM | SUP_SYSTEMES | INRIA | SUP_LSS | CENTRALESUPELEC | L2S | UNIV-PARIS-SACLAY | CRISTAL-SYNER | IMT-LILLE-DOUAI | CRISTAL | UNIV-LILLE

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Hassan Omran, Laurentiu Hetel, Mihaly Petreczky, Jean-Pierre Richard, Francoise Lamnabhi-Lagarrigue. Stability analysis of some classes of input-affine nonlinear systems with aperiodic sampled-data control. Automatica, Elsevier, 2016, 70, pp.266-274. ⟨10.1016/j.automatica.2016.02.013⟩. ⟨hal-01343851⟩

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