Observer design for a class of nonlinear time-delay systems

In this paper, we investigate a new method for the observer design problem for a class of nonlinear time-delay systems. The main contribution lies in the use of a new structure for the proposed observer. This new structure has as objective to obtain an approach applicable on a large class of nonlinear time-delay systems and to reduce the conservatism of the synthesis condition ensuring the exponential convergence of the estimation error towards zero. The stability analysis is performed using a Lyapunov-Krasovskii functional that leads to the solvability of a matrix inequality, which becomes linear (LMI) whenever an unknown scalar variable is chosen a priori. A numerical example is presented in order to show the efficiency of our method.