Observers for the class of differentiable Lipschitz nonlinear systems

In this paper, the full-order and reduced-order observer design for a class of so-called differential Lipschitz nonlinear systems is investigated. Based on the differential mean value theorem (DMVT) and an important matrix inequality, we propose sufficient conditions for the existence of the observers of the class of nonlinear systems. The proposed sufficient conditions are given in terms of linear matrix inequalities (LMIs). We obtain a sufficient condition which is less conservative than those given in literature for reduced-order observer design of a class of nonlinear systems. By comparison with Zemouche et al. [Observers for a class of Lipschitz systems with extension to H_∞ performance analysis, System & Control Letters, 57 (2008), 18-27] the proposed approach avoids solving high-order LMI. The solvability of the proposed LMI is better than that of the matrix inequality given in literature. Some examples are given to illustrate the proposed approach.