A Note on Observers for Discrete-Time Lipschitz Nonlinear Systems

This brief considers observer design for a class of discrete-time nonlinear systems with Lipschitz nonlinearities. We first remark some statements and results in a recent brief by Zemouche and Boutayeb. In particular, we show that their results are more conservative than an existing one, rather than less conservative as claimed. Moreover, most of the existing results are only applicable to some particular classes of Lipschitz systems with a Lipschitz constant less than one. In order to obtain less conservative results, the concept of a one-sided Lipschitz condition, which is an extension of its well-known Lipschitz counterpart, is introduced. Sufficient conditions ensuring the existence of state observers for one-sided Lipschitz nonlinear systems are then presented. A numerical example is included to illustrate the advantages and effectiveness of the proposed design.