Optimal reset adaptive observer design

A reset adaptive observer (ReAO) is an adaptive observer consisting of an integrator and a reset law that resets the output of the integrator depending on a predefined reset condition. The inclusion of reset elements can improve the observer performance but it can also destroy the stability of the estimation process if the ReAO is not properly tuned. As contribution, a method to optimally tune the parameters and gains of the ReAO is presented. They are optimally chosen by solving the L2L2 gain minimization problem, which can be rewritten as an equivalent LMI problem. The effectiveness of the proposed method is checked by simulations comparing the results of an optimal ReAO with an optimal traditional adaptive observer.