State estimation for discrete-time systems with generalized Lipschitz nonlinear dynamics

This paper considers the state estimation problem for a class of discrete-time systems with generalized Lipschitz nonlinear dynamics. Under the assumption that the system nonlinearities satisfy a quadratically inner-boundedness condition, we design both the full-order observer and the reduced-order observer for the discrete-time nonlinear system. Sufficient conditions ensuring the existence of full-order observers as well as reduced-order observers for such systems are established and formulated in terms of linear matrix inequality (LMI). Compared with some existing results, we remove the one-sided Lipschitz restrict and extend the classical Lipschitz observer design to a larger class of discrete-time nonlinear systems. A numerical example is included to illustrate the effectiveness of the proposed design.