Observers Ofr The Class Of Difforcntiable Lipschitz Nonlinear Systems

In this paper, the full-and reduced-order observer design for a class of so-called diferential Lipschitz nonlinear systems is investigated. Based on the dif-ferential mean value theorem (DMV T) and an important matrix inequality, wepropose sufcient conditions for the existence of the observers of the class of nonlin-ear systems. The proposed sufcient conditions are given in terms of linear matrixinequalities (LMI), and they are complements of the sufcient conditions givenin literature at least. In addition, we obtain a sufcient condition which is lessconservative than those given in literature for reduced-order observer design of aclass of nonlinear systems. By comparison with Zemouche et al.[Observers for aclass of Lipschitz systems with extension to H∞performance analysis, System&Control Letters,57(2008),18-27] the proposed approach avoids solving high-orderLMI. The solvability of the proposed LMI is better than that of the matrixinequality given in literature. Also, the proposed approach avoids high gain for aclass of triangular globally Lipschitz systems. Some examples are given to illustratethe proposed approach.