Nonlinear observer design for a class of Lipschitz time-delay systems with unknown inputs: LMI approach

In this paper, we consider a method to design a full-order nonlinear observer for a class of nonlinear time-delay systems with unknown inputs. Based on Lyapunov-Krasovskii functional, we derive a sufficient condition for existence of the designed observer which requires solving a set of nonlinear matrix inequalities. Then, the achieved condition is formulated in terms of two linear matrix inequalities (LMIs). Finally, the proposed observer is illustrated with an example.