Bounded Extremum Seeking for Static Quadratic Maps Using Nonlinear Transformation and Lyapunov Method

We present a new practical stability analysis for a bounded gradient based extremum seeking problem for two variable static quadratic maps that contain a time-varying additive measurement uncertainty. Instead of using earlier averaging-based approaches, we introduce a new state transformation, a time-varying quadratic Lyapunov function, and a comparison principle to obtain essentially less conservative bounds on the dither frequency and on the ultimate bound of the estimation error compared with earlier results. Our numerical example illustrates the efficiency of the method.