Reset adaptive observers and stability properties

This paper proposes a novel kind of adaptive observer 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 paper is the application of the reset element theory to the adaptive observer LTI framework. The introduction of the reset element in the adaptive laws 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 also addressed. Additionally, an easily computable method to determine the ℒ2 gain of the ReO dealing with noise-corrupted systems is presented. A simulation example shows the potential benefit of the proposed reset adaptive observer.