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Analytical solutions to feedback systems on the special orthogonal group SO(n)
Markdahl, J.; Thunberg, Johan; Hoppe, J. et al.
2013In the proceeding of the 52nd Annual Conference on Decision and Control
Peer reviewed
 

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Abstract :
[en] This paper provides analytical solutions to the closed-loop kinematics of two almost globally exponentially stabilizing attitude control laws on the special orthogonal group SO(n). By studying the general case we give a uniform treatment to the cases of SO(2) and SO(3), which are the most interesting dimensions for application purposes. Working directly with rotation matrices in the case of SO(3) allows us to avoid certain complications which may arise when using local and global many-to-one parameterizations. The analytical solutions provide insight into the transient behaviour of the system and are of theoretical value since they can be used to prove almost global attractiveness of the identity matrix. The practical usefulness of analytical solutions in problems of continuous time actuation subject to piece-wise unavailable or discrete time sensing are illustrated by numerical examples.
Disciplines :
Engineering, computing & technology: Multidisciplinary, general & others
Author, co-author :
Markdahl, J.
Thunberg, Johan ;  University of Luxembourg > Luxembourg Centre for Systems Biomedicine (LCSB)
Hoppe, J.
Hu, X.
External co-authors :
yes
Language :
English
Title :
Analytical solutions to feedback systems on the special orthogonal group SO(n)
Publication date :
2013
Event name :
52nd Annual Conference on Decision and Control
Event place :
Firenze, Italy
Event date :
10-13 December, 2013
Main work title :
the proceeding of the 52nd Annual Conference on Decision and Control
Publisher :
IEEE
Pages :
5246-5251
Peer reviewed :
Peer reviewed
Available on ORBilu :
since 31 March 2015

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