1. Exponential Stability Analysis of Sampled-data ODE-PDE Systems and Application to Observer Design
- Author
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Ahmed-Ali, Tarek, Karafyllis, Iasson, Giri, Fouad, Krstic, Miroslav, Lamnabhi-Lagarrigue, Françoise, Equipe Automatique - Laboratoire GREYC - UMR6072, Groupe de Recherche en Informatique, Image et Instrumentation de Caen (GREYC), Centre National de la Recherche Scientifique (CNRS)-École Nationale Supérieure d'Ingénieurs de Caen (ENSICAEN), Normandie Université (NU)-Normandie Université (NU)-Université de Caen Normandie (UNICAEN), Normandie Université (NU)-Centre National de la Recherche Scientifique (CNRS)-École Nationale Supérieure d'Ingénieurs de Caen (ENSICAEN), Normandie Université (NU), National Technical University of Athens [Athens] (NTUA), Laboratoire des signaux et systèmes (L2S), Université Paris-Sud - Paris 11 (UP11)-CentraleSupélec-Centre National de la Recherche Scientifique (CNRS), and Baverel, Myriam
- Subjects
[SPI.AUTO] Engineering Sciences [physics]/Automatic ,[INFO.INFO-AU]Computer Science [cs]/Automatic Control Engineering ,[INFO.INFO-AU] Computer Science [cs]/Automatic Control Engineering ,[SPI.AUTO]Engineering Sciences [physics]/Automatic - Abstract
International audience; A small-gain approach is presented for analyzing exponential stability of a class of (dynamical) hybrid systems. The systems considered in the paper are composed of finite-dimensional dynamics, represented by a linear Ordinary Differential Equation (ODE), and infinite-dimensional dynamics described by a parabolic Partial Differential Equation (PDE). Exponential stability is established under conditions involving the maximum allowable sampling period (MASP). This new stability result is shown to be useful in the design of sampled-output exponentially convergent observers for linear systems that are described by an ODE-PDE cascade. The new stability result also proves to be useful in designing practical approximate observers involving no PDEs. Index Terms-ODE-PDE cascade systems, sampled-data systems, observer design, backstepping approach, exponentially convergent observers.
- Published
- 2016