Compact perturbations of controlled systems
| Autor: | Guillaume Olive, Michel Duprez |
|---|---|
| Přispěvatelé: | Institut de Mathématiques de Marseille (I2M), Aix Marseille Université (AMU)-École Centrale de Marseille (ECM)-Centre National de la Recherche Scientifique (CNRS), Institut de Mathématiques de Bordeaux (IMB), Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS), Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1 (UB)-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS) |
| Rok vydání: | 2018 |
| Předmět: |
0209 industrial biotechnology
Lemma (mathematics) Control and Optimization Applied Mathematics 010102 general mathematics Linear system Exact controllability Compactness-uniqueness 02 engineering and technology Characterization (mathematics) [MATH.MATH-FA]Mathematics [math]/Functional Analysis [math.FA] 01 natural sciences Reachable states System a MSC 93B05 93C73 93C73 Set (abstract data type) Controllability Fattorini-Hautus test 020901 industrial engineering & automation Control theory [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP] Applied mathematics [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC] 0101 mathematics Mathematics |
| Zdroj: | Mathematical Control and Related Fields Mathematical Control and Related Fields, AIMS, 2018, 8 (2), pp.397-410 Mathematical Control and Related Fields, 2018, 8 (2), pp.397-410 |
| ISSN: | 2156-8499 2156-8472 |
| DOI: | 10.3934/mcrf.2018016 |
| Popis: | International audience; In this article we study the controllability properties of general compactly perturbed exactly controlled linear systems with admissible control operators. Firstly, we show that approximate and exact controllability are equivalent properties for such systems. Then, and more importantly, we provide for the perturbed system a complete characterization of the set of reachable states in terms of the Fattorini-Hautus test. The results rely on the Peetre lemma. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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