Continuous but non-smooth adaptive observer of a class of nonlinear systems

In this paper, we study continuous but non-smooth adaptive observer of a class of nonlinear systems. Compared with the traditional adaptive observers, there is an additional homogeneous nonlinear part. The additional part can not only accelerate the convergent speed of the estimation errors of the states and the unknown parameters, but also improve robust against additional noises. The main results are derived by using the geometric homogeneity theory and the high gain techniques. The results can also been extended to nonlinear systems with nonlinear parameterization. Numerical simulation is used to show the efficiency of the new methods.