Estimation of the basin of attraction of a practical high-gain observer

In this paper, a technique is given to estimate the basin of attraction of a 'practical' high-gain observer for polynomial autonomous systems. Such a goal is pursued by determining a set such that the restriction of the observability map of the system to such a set is a diffeomorphism. Differently from other techniques available in the literature, which are based on the numeric computation of the trajectories of a system corresponding to the observability map, the proposed procedure provides exact certificates of invertibility of the observability map. The application of the proposed method to the design of a nonlinear observer is discussed.