Control Systems and Number Theory
Author
Source
International Journal of Mathematics and Mathematical Sciences
Issue
Vol. 2012, Issue 2012 (31 Dec. 2012), pp.1-28, 28 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2012-02-20
Country of Publication
Egypt
No. of Pages
28
Main Subjects
Abstract EN
We try to pave a smooth road to a proper understanding of control problems in terms of mathematical disciplines, and partially show how to number-theorize some practical problems.
Our primary concern is linear systems from the point of view of our principle of visualization of the state, an interface between the past and the present.
We view all the systems as embedded in the state equation, thus visualizing the state.
Then we go on to treat the chain-scattering representation of the plant of Kimura 1997, which includes the feedback connection in a natural way, and we consider the H∞-control problem in this framework.
We may view in particular the unit feedback system as accommodated in the chain-scattering representation, giving a better insight into the structure of the system.
Its homographic transformation works as the action of the symplectic group on the Siegel upper half-space in the case of constant matrices.
Both of H∞- and PID-controllers are applied successfully in the EV control by J.-Y.
Cao and B.-G.
Cao 2006 and Cao et al.
2007, which we may unify in our framework.
Finally, we mention some similarities between control theory and zeta-functions.
American Psychological Association (APA)
Li, Fuhuo. 2012. Control Systems and Number Theory. International Journal of Mathematics and Mathematical Sciences،Vol. 2012, no. 2012, pp.1-28.
https://search.emarefa.net/detail/BIM-477245
Modern Language Association (MLA)
Li, Fuhuo. Control Systems and Number Theory. International Journal of Mathematics and Mathematical Sciences No. 2012 (2012), pp.1-28.
https://search.emarefa.net/detail/BIM-477245
American Medical Association (AMA)
Li, Fuhuo. Control Systems and Number Theory. International Journal of Mathematics and Mathematical Sciences. 2012. Vol. 2012, no. 2012, pp.1-28.
https://search.emarefa.net/detail/BIM-477245
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-477245