On adaptive observers design for a class of uniformly observable systems

In this paper, one aims at addressing the adaptive observer design for a class of multivariable nonlinear systems with Lipschitz nonlinearities. Two adaptive observers have been derived using two different approaches issued from an overview of the available adaptive observer design literature. The first one is a natural extension of a recently proposed adaptive observer for single output systems, while the second one has been derived bearing in mind the fact that an adaptive observer can be derived using a high gain state observer design approach based on an augmented system model accounting for the unknown parameter dynamics. Both observers are shown to be equivalent in the sens that they are governed by the same equations and the underlying exponential convergences of state observation and parameter estimation errors are insured under the the same persistent excitation condition.