Robust observers design for a class of nonlinear discrete-time systems

This paper deals with the problem of stability analysis of the Extended Kalman Filter (EKF) when used as an observer for the class of non linear discrete-time systems with linear output map. The proposed technique uses the Lyapnnov approach and evaluates the propagation errors due to the first order linearisation. Sufficient conditions to ensure robust stability of the modified gain EKF are established. One of the main features in this paper is how to design an instrumental matrix, namely R_k in the paper. in order to enlarge domain of attraction and to improve the convergence significantly. To show performances and accuracy of the proposed algorithm, it will be applied to a physical process largely used in the literature.