Delay effects and dynamical compensation for time-delay systems

We develop an observer-based H/sup /spl infin// controller for linear time delay systems. The main contribution is to provide a closed loop stability analysis for the general case when the system time delay is unknown. Our analysis is based on model transformation and on a comparison principle. This allows us to get delay dependent stabilizing conditions. We derive conditions which improve (or recover) previous results. Comments on the conservatism of the presented criteria are given. The approach makes use of appropriate Liapunov-Krasovskii functionals and the obtained criteria are expressed in terms of linear matrix inequalities. A numerical example illustrates this method.