On Some Relations between Accretive, Positive, and Pseudocontractive Operators and Passivity Results in Hilbert Spaces and Nonlinear Dynamic Systems
Author
Source
Discrete Dynamics in Nature and Society
Issue
Vol. 2017, Issue 2017 (31 Dec. 2017), pp.1-17, 17 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2017-10-04
Country of Publication
Egypt
No. of Pages
17
Main Subjects
Abstract EN
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.
American Psychological Association (APA)
de La Sen, Manuel. 2017. 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،Vol. 2017, no. 2017, pp.1-17.
https://search.emarefa.net/detail/BIM-1151126
Modern Language Association (MLA)
de La Sen, Manuel. 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 No. 2017 (2017), pp.1-17.
https://search.emarefa.net/detail/BIM-1151126
American Medical Association (AMA)
de La Sen, Manuel. 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. 2017. Vol. 2017, no. 2017, pp.1-17.
https://search.emarefa.net/detail/BIM-1151126
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1151126