We consider bounded extremum seeking controls for time-varying linear systems with uncertain coefficient matrices and measurement uncertainty. Using a new change of variables, Lyapunov functions, and a comparison principle, we provide semiglobal exponential stability bounds for the states of the closed loop systems that hold for all nonnegative times. For the first time, we consider bounded extremum seeking controls in the presence of constant input delays and for linear time-varying systems with unknown control directions, and we provide reduction model controllers for quantifying the effects of the delays.
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Mazenc et al. (2024) studied this question.
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