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Singularly Perturbed Lie Bracket Approximation
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DOI：10.1109/TAC.2015.2416925.png)
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Abstract
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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:
Extremum seeking
Lie brackets
singular perturbations
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