Observer analysis and design for nonlinear bounded Lipschitz systems

The design of dynamic observers for nonlinear Lipschitz systems has considered great attention in past decades. Instead of applying the standard strictly explicit designs or LMI-based heuristic solutions, in this paper, an efficient systematic method is deployed by considering the existence of some arbitrary bounds on the nonlinear Lipschitz terms. The method enables to relax the observer design from the conventional restrictions and it is easily solved analytically without needing the solution of LMIs. As proven in the paper by a detailed and rigorous analysis, its main advantage is that it guarantees global asymptotic stability and ensures the observer response with desired decay characteristics satisfying simultaneously the Lyapunov equation.