DocumentCode :
189535
Title :
Noncommutative geometric structures on stabilizable infinite-dimensional linear systems
Author :
Quadrat, Alban
Author_Institution :
Inria Saclay - Ile-de-France, Supelec, Gif-sur-Yvette, France
fYear :
2014
fDate :
24-27 June 2014
Firstpage :
2460
Lastpage :
2465
Abstract :
This paper aims at showing that noncommutative geometric structures such as connections and curvatures exist on internally stabilizable infinite-dimensional linear systems and on their stabilizing controllers. To see this new geometry, using the noncommutative geometry developed by Connes, we have to replace the standard differential calculus by the quantized differential calculus and classical vector bundles by projective modules. We give an explicit description of the connections on an internally stabilizable system and on its stabilizing controllers in terms of the projectors of the closed-loop system classically used in robust control. These connections aim at studying the variations of the signals in the closed-loop system in response to a disturbance or a change of the reference. We also compute the curvatures of these connections.
Keywords :
closed loop systems; differentiation; geometry; linear systems; multidimensional systems; robust control; closed-loop system; explicit connection description; internally stabilizable infinite-dimensional linear systems; noncommutative geometric structures; projective modules; quantized differential calculus; robust control; stabilizing controllers; Geometry; Sensitivity; Standards; Transfer functions; Vectors;
fLanguage :
English
Publisher :
ieee
Conference_Titel :
Control Conference (ECC), 2014 European
Conference_Location :
Strasbourg
Print_ISBN :
978-3-9524269-1-3
Type :
conf
DOI :
10.1109/ECC.2014.6862563
Filename :
6862563
Link To Document :
بازگشت