On adaptive observers design for a class of uniformly observable systems

International audienceIn this paper, one aims at addressing the adaptive observer design for a class of multivariablenonlinear 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 oneis a natural extension of a recently proposed adaptive observer for single output systems, while the second one has been derived bearing inmind the fact that an adaptive observer can be derived using a high gain sate observer design approach based on an augmented system model accountingfor 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 convergence of state observation and parameter estimation errors are insured under the the same persistent excitation condition