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INTRODUCTION TO SEMIGROUP THEORY
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UNSPECIFIED. (1993) INTRODUCTION TO SEMIGROUP THEORY. LECTURE NOTES IN CONTROL AND INFORMATION SCIENCES, 185 . pp. 122. ISSN 01708643
Full text not available from this repository.Abstract
In this paper some basic sytem theoretic concepts will be introduced for abstract systems of the form x(t) = Ax(t) + Bu(t), x(0) = x0, y(t) = Cx(t). (1)
Here A is the infinitesimal generator of a strongly continuous semigroup S(t) on a Banach space Z and necessary and sufficient conditions for this to be the case axe given by the HilleYosida theorem. For U another Banach space B isanelementof C(U, Z) and x0 isanelementof Z, u(.) isanelementof L2(0, infinity; U) a mild solution is defined to be x(t) = S(t)x0 + integralt/0 S(t  s)Bu(s)ds (2) and x(.) isanelementof C(0; infinity; Z). Various definitions of controllablity, observability, stabilizability, detectability, identifiability and realizability will be given and theorems which characterize them will be stated. Throughout the paper examples will be given (albeit trivial ones) which illustrate the way the abstract definitions and results can be applied to concrete problems defined via partial differential equations and delay equations.
In preparing this introduction I have made considerable use of the following book by Ruth Curtain and Hans Zwart An Introduction to Infinite Dimensional Linear Systems Theory which is to be published soon.
Item Type:  Journal Article  

Subjects:  Q Science > QA Mathematics > QA76 Electronic computers. Computer science. Computer software T Technology > TL Motor vehicles. Aeronautics. Astronautics 

Journal or Publication Title:  LECTURE NOTES IN CONTROL AND INFORMATION SCIENCES  
Publisher:  SPRINGER VERLAG  
ISSN:  01708643  
Official Date:  1993  
Dates: 


Volume:  185  
Number of Pages:  22  
Page Range:  pp. 122  
Publication Status:  Published  
URI:  http://wrap.warwick.ac.uk/id/eprint/21273 
Data sourced from Thomson Reuters' Web of Knowledge
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