Observer design for lipschitz nonlinear systems: The discrete-time case

This brief deals with observer design for a class of discrete-time nonlinear systems, namely, linear systems with Lipschitz nonlinearities. Perhaps one of the main features, with respect to the existing results, is the use of new particular Lyapunov functions to deduce nonconservative conditions for asymptotic convergence of the state estimation errors. The established sufficient conditions are expressed in terms of linear matrix inequalities, which are easily and numerically tractable by standard software algorithms. By means of simple transformations, a reduced-order version is established where the observer gain is computed in an optimal manner. Performances of the proposed approach are illustrated through simulation and experimental results; one of them concerns synchronization of chaotic nonlinear models.