Reduced-order observer design for one-sided Lipschitz non-linear systems

In this paper, the reduced-order observer design for a class of non-linear systems is investigated. Based on the one-sided Lipschitz condition, we present sufficient conditions for the existence of the reduced-order observers of the class of non-linear systems, these conditions are less conservative than those based on Lipschitz condition in literature. It should be noted that the one-sided Lipschitz condition is directly applicable to the important class of the Lipschitz non-linear systems. In considering many problems, the present paper obtains the one-sided Lipschitz constants that are significantly smaller than the classical Lipschitz constants (see Appendix). Some examples are given to illustrate effects of the proposed approach. The last example is introduced with the goal, to illustrate our proposed method to be effective for the important class of the Lipschitz non-linear systems.