DocumentCode
3601694
Title
Singularly Perturbed Lie Bracket Approximation
Author
Durr, Hans-Bernd ; Krstic, Miroslav ; Scheinker, Alexander ; Ebenbauer, Christian
Author_Institution
Inst. for Syst. Theor. & Autom. Control, Univ. of Stuttgart, Stuttgart, Germany
Volume
60
Issue
12
fYear
2015
Firstpage
3287
Lastpage
3292
Abstract
We consider the interconnection of two dynamical systems where one has an input-affine vector field. By employing a singular perturbation and a Lie bracket analysis technique, we show how the trajectories can be approximated by two decoupled systems. From this trajectory approximation result and the stability properties of the decoupled systems, we derive stability properties of the overall system.
Keywords
Lie algebras; interconnected systems; singularly perturbed systems; stability; trajectory control; Lie bracket analysis technique; decoupled systems; dynamical system interconnection; input-affine vector field; singularly perturbed lie bracket approximation; stability properties; trajectory approximation; Approximation methods; Asymptotic stability; Computational modeling; Indexes; Stability criteria; Trajectory; Extremum seeking; Lie brackets; singular perturbations;
fLanguage
English
Journal_Title
Automatic Control, IEEE Transactions on
Publisher
ieee
ISSN
0018-9286
Type
jour
DOI
10.1109/TAC.2015.2416925
Filename
7070696
Link To Document