Singularly Perturbed Lie Bracket Approximation

Journal Article · 27 March 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 Laboratory (LANL), Los Alamos, NM (United States)
• Sponsoring Organization: USDOE; German Research Foundation (DFG)
• Grant/Contract Number: AC52-06NA25396
• OSTI ID: 1351223
• Report Number(s): LA-UR-15-27668
• Journal Information: IEEE Transactions on Automatic Control, Vol. 60, Issue 12; ISSN 0018-9286
• Publisher: IEEECopyright Statement
• Country of Publication: United States
• Language: English