Control systems and number theory
type: Item
instance of: scholarly article
title: Control systems and number theory
zbMATH Open document ID: 1238.93032
DOI: 10.1155/2012/508721
author: Fuhuo Li
published in: International Journal of Mathematics and Mathematical Sciences
publication date: 2012-05-14T00:00:00Z
review text: Summary: 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 directed to 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 \(H^\infty\)-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, \(H^\infty\)- 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.
Mathematics Subject Classification ID: 93B36
Mathematics Subject Classification ID: 93B25
zbMATH DE Number: 6034285
zbMATH Keywords: linear systems
zbMATH Keywords: chain-scattering representation of the plant
zbMATH Keywords: \(H^\infty\)-control
zbMATH Keywords: unit feedback system
zbMATH Keywords: symplectic group on the Siegel upper half-space
Wikidata QID: Q58704792
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2012/508721
OpenAlex ID: W1971039626
cites work: Q3594584
cites work: Wigert's approximate functional equation and the Riemann zeta-function
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cites work: Non-Euclidean functional analysis and electronics
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DBLP publication ID: journals/ijmmsc/Li12
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description: scientific article; zbMATH DE number 6034285