Observer scheme for linear recycling systems with time delays

In this paper a new control methodology is proposed for unstable linear time-delay systems with recycle. For this kind of systems time delays are present in the forward and backward paths increasing control difficulty. The strategy is based on the observation that if some internal system signals were known then it would be possible to remove the backward dynamics. In this way, a controller feedback could be designed by considering only the dynamics of the forward loop. To carry out this strategy an asymptotic observer is proposed to estimate the internal signals needed. Necessary and sufficient conditions to assure convergence of the proposed observer predictor are given. An overall procedure for the proposed methodology is provided and numerical simulations to illustrate its performance are presented.