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
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;
Journal_Title :
Automatic Control, IEEE Transactions on
DOI :
10.1109/TAC.2015.2416925
