Traditionally, sinusoidally perturbed extremum seeking (ES) schemes utilise a gradient descent adaptation law to update the mean control input toward the optimising set point. The tuneable gain, k, in this adaptation law must be chosen sufficiently small to guarantee convergence but as large as possible to ensure fast convergence. However, previous analyses are unable to explicitly provide the upper bound on k guaranteeing convergence. Here, an observer based ES approach is used within a particular ES framework for a static plant. Deviating from the classical sinusoidally perturbed ES approach, specific plant information is assumed to be available and this results in an analytical estimate of the upper bound on k for non-local stability. The conservativeness of this estimate is investigated in simulations.
