On Some Relations between Accretive, Positive, and Pseudocontractive Operators and Passivity Results in Hilbert Spaces and Nonlinear Dynamic Systems
This paper investigates some parallel relations between the operators I-G and G in Hilbert spaces in such a way that the pseudocontractivity, asymptotic pseudocontractivity, and asymptotic pseudocontractivity in the intermediate sense of one of them are equivalent to the accretivity, asymptotic accr...
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| Format: | Article |
| Language: | English |
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Wiley
2017-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2017/1497867 |
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| author | M. De la Sen |
| author_facet | M. De la Sen |
| author_sort | M. De la Sen |
| collection | DOAJ |
| description | This paper investigates some parallel relations between the operators I-G and G in Hilbert spaces in such a way that the pseudocontractivity, asymptotic pseudocontractivity, and asymptotic pseudocontractivity in the intermediate sense of one of them are equivalent to the accretivity, asymptotic accretivity, and asymptotic accretivity in the intermediate sense of the other operator. If the operators are self-adjoint then the obtained accretivity-type properties are also passivity-type properties. Such properties are very relevant in stability theory since they refer to global stability properties of passive feed-forward, in general, nonlinear, and time-varying controlled systems controlled via feedback by elements in a very general class of passive, in general, nonlinear, and time-varying controllers. These results allow the direct generalization of passivity results in controlled dynamic systems to wide classes of tandems of controlled systems and their controllers, described by G-operators, and their parallel interpretations as pseudocontractive properties of their counterpart I-G-operators. Some of the obtained results are also directly related to input-passivity, output-passivity, and hyperstability properties in controlled dynamic systems. Some illustrative examples are also given in the framework of dynamic systems described by extended square-integrable input and output signals. |
| format | Article |
| id | doaj-art-13f6d5156a9d48fb92069282f87cd828 |
| institution | OA Journals |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2017-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-13f6d5156a9d48fb92069282f87cd8282025-08-20T02:04:51ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2017-01-01201710.1155/2017/14978671497867On Some Relations between Accretive, Positive, and Pseudocontractive Operators and Passivity Results in Hilbert Spaces and Nonlinear Dynamic SystemsM. De la Sen0Institute of Research and Development of Processes IIDP, Faculty of Science and Technology, University of the Basque Country, P.O. Box 644 de Bilbao, Barrio Sarriena, Leioa, 48940 Bizkaia, SpainThis paper investigates some parallel relations between the operators I-G and G in Hilbert spaces in such a way that the pseudocontractivity, asymptotic pseudocontractivity, and asymptotic pseudocontractivity in the intermediate sense of one of them are equivalent to the accretivity, asymptotic accretivity, and asymptotic accretivity in the intermediate sense of the other operator. If the operators are self-adjoint then the obtained accretivity-type properties are also passivity-type properties. Such properties are very relevant in stability theory since they refer to global stability properties of passive feed-forward, in general, nonlinear, and time-varying controlled systems controlled via feedback by elements in a very general class of passive, in general, nonlinear, and time-varying controllers. These results allow the direct generalization of passivity results in controlled dynamic systems to wide classes of tandems of controlled systems and their controllers, described by G-operators, and their parallel interpretations as pseudocontractive properties of their counterpart I-G-operators. Some of the obtained results are also directly related to input-passivity, output-passivity, and hyperstability properties in controlled dynamic systems. Some illustrative examples are also given in the framework of dynamic systems described by extended square-integrable input and output signals.http://dx.doi.org/10.1155/2017/1497867 |
| spellingShingle | M. De la Sen On Some Relations between Accretive, Positive, and Pseudocontractive Operators and Passivity Results in Hilbert Spaces and Nonlinear Dynamic Systems Discrete Dynamics in Nature and Society |
| title | On Some Relations between Accretive, Positive, and Pseudocontractive Operators and Passivity Results in Hilbert Spaces and Nonlinear Dynamic Systems |
| title_full | On Some Relations between Accretive, Positive, and Pseudocontractive Operators and Passivity Results in Hilbert Spaces and Nonlinear Dynamic Systems |
| title_fullStr | On Some Relations between Accretive, Positive, and Pseudocontractive Operators and Passivity Results in Hilbert Spaces and Nonlinear Dynamic Systems |
| title_full_unstemmed | On Some Relations between Accretive, Positive, and Pseudocontractive Operators and Passivity Results in Hilbert Spaces and Nonlinear Dynamic Systems |
| title_short | On Some Relations between Accretive, Positive, and Pseudocontractive Operators and Passivity Results in Hilbert Spaces and Nonlinear Dynamic Systems |
| title_sort | on some relations between accretive positive and pseudocontractive operators and passivity results in hilbert spaces and nonlinear dynamic systems |
| url | http://dx.doi.org/10.1155/2017/1497867 |
| work_keys_str_mv | AT mdelasen onsomerelationsbetweenaccretivepositiveandpseudocontractiveoperatorsandpassivityresultsinhilbertspacesandnonlineardynamicsystems |