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We analyze stability and robustness properties of an extremum seeking schemethat employs oscillatory dither signals with sufficiently large amplitudes andfrequencies. Our study takes both input and output disturbances into account.We consider general $L_\infty$-disturbances, which may resonate with theoscillatory dither signals. A suitable change of coordinates followed by anaveraging procedure reveals that the closed-loop system approximates thebehavior of an averaged system. This leads to the effect that stability androbustness properties carry over from the averaged system to the closed-loopsystem. In particular, we show that, if the averaged system is input-to-statestable (ISS), then the closed-loop system has ISS-like properties.

Robustness properties of a large-amplitude, high-frequency extremum seeking control scheme