Observer design for a class of Lipschitz time-delay systems

This paper deals with observers design of non-linear time-delay systems. We investigate in particular, a useful technique based on the use of the Differential MeanValue Theorem (DMVT) and the Lyapunov-Krasovskii functionals to give a very suitable sufficient synthesis condition to assure exponential convergence. The obtained condition is formulated in terms of matrix inequality which becomes linear whenever an unknown scalar is chosen a priori. On the other hand, we introduce a simple and relevant transformation to show how to extend the obtained results to a particular class of continuous but non-differentiable systems. To show performances of the proposed approach and the large class of systems that may be concerned, numerical examples are provided.