Bounded extremum seeking for static maps with large measurement delay and measurement bias

In this paper, we present a time-delay approach to bounded extremum seeking (BES) for an uncertain n-dimensional static quadratic maps in the presence of large constant measurement delay and measurement bias. We assume that uncertain Hessian is from a known range. Given any delay, we derive constructive conditions for practical stability of the ES system in terms of simple scalar linear inequalities for finding tuning parameters that guarantee the convergence. To manage with large delays in the high amplitude BES, we choose small gains that lead to slow decay rates, but guarantee robustness with respect to measurement bias. We show that given any delays, any upper bound of bias's derivative and any initial box, we can find a lower bound on the dither frequency that ensures practical stability.