Singularly Perturbed Lie Bracket Approximation

Journal Article · Fri Mar 27 00:00:00 UTC 2015 · IEEE Transactions on Automatic Control

DOI:https://doi.org/10.1109/TAC.2015.2416925· OSTI ID:1351223

Durr, Hans-Bernd ^[1]; Krstic, Miroslav ^[2]; Scheinker, Alexander ^[3]; Ebenbauer, Christian ^[1]

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1. Univ. of Stuttgart (Germany). Inst. for Systems Theory and Automatic Control
2. Univ. of California, San Diego, CA (United States). Cymer Center for Control Systems and Dynamics, Dept. of Mechanical and Aerospace Engineering
3. Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

Here, we consider the interconnection of two dynamical systems where one has an input-affine vector field. We show that by employing a singular perturbation analysis and the Lie bracket approximation technique, the stability of the overall system can be analyzed by regarding the stability properties of two reduced, uncoupled systems.

• Research Organization: Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
• Sponsoring Organization: Deutsche Forschungsgemeinschaft; USDOE
• Grant/Contract Number: AC52-06NA25396
• OSTI ID: 1351223
• Report Number(s): LA-UR--15-27668
• Journal Information: IEEE Transactions on Automatic Control, Journal Name: IEEE Transactions on Automatic Control Journal Issue: 12 Vol. 60; ISSN 0018-9286
• Publisher: IEEE
• Country of Publication: United States
• Language: English

Related Subjects

97 MATHEMATICS AND COMPUTING
Approximation methods
Asymptotic stability
Computational modeling
Extremum seeking
Indexes
Lie brackets
Mathematics
Stability criteria
Trajectory
singular perturbations