Reset Adaptive Observer for a Class of Nonlinear Systems

This technical note proposes a novel kind of state estimator called reset adaptive observer (ReO). A ReO is an adaptive observer consisting of an integrator and a reset law that resets the output of the integrator depending on a predefined condition. The main contribution of this technical note is that the reset element theory is applied for the first time to the nonlinear adaptive observer framework. The introduction of the reset element in the adaptive law can decrease the overshooting and settling time of the estimation process without sacrificing the rising time. The stability and convergence LMI-based analysis of the proposed ReO is addressed and, additionally, an easily computable method to determine the L₂ gain of the ReO dealing with noise-corrupted systems is presented.