Design of a nonlinear adaptive observer for a class of Lipschitz systems

This paper considers the nonlinear adaptive observer design problem of a class of Lipschitz systems. The parameter and state estimation in the presence of the observer gain perturbations for Lipschitz systems that are linear in the unknown parameters and nonlinear in state are addressed. Using Lyapunov functions and functionals, conditions have been found that guarantee the asymptotic stability of the estimation error. The gain for the observer can be conveniently derived by means of Linear Matrix Inequality.