On the necessity of looped-functionals arising in the analysis of pseudo-periodic,sampled-data and hybrid systems |
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Authors: | Corentin Briat Alexandre Seuret |
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Affiliation: | 1. Department of Biosystems Science and Engineering, Swiss Federal Institute of Technology–Zürich, Basel, Switzerlandcorentin@briat.info;3. CNRS, LAAS, 7 avenue du colonel Roche, F-31400 Toulouse, France and Univ de Toulouse, LAAS, F-31400 Toulouse, France |
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Abstract: | Looped-functionals have been shown to be relevant for the analysis of a wide variety of systems. However, the conditions obtained in previous papers on the analysis of sampled-data, impulsive and switched systems have only been shown to be sufficient for the characterisation of their associated discrete-time stability conditions. We prove here that these conditions are also necessary. This result is derived for a wider class of linear systems, referred to as impulsive pseudo-periodic systems, that encompass periodic, impulsive, sampled-data and switched systems as special cases. |
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Keywords: | looped-functionals periodic systems sampled-data systems hybrid systems |
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