Use of asymptotic observers having-high-gains in the state and parameter estimation

The estimation of the unknown parameters of a nonlinear system is reduced to the estimation of its state variables by a state-space immersion. The Luenberger observer is used in the state estimation of the extended nonlinear system. The use of high gains in the cancellation of nonlinearities in order to simplify the observer design is studied. The high gain induces a time-scale separation between the nonlinear system and the observer, and therefore the singular perturbation theory can be used in the stability analysis of the error dynamics. In particular, it is shown that the error dynamics reaches stable equilibrium very fast, ensuring that the slow dynamics of the observer is just that of the given nonlinear system