Control of unstable delayed recycling systems

This work deals with the stabilization of recycling systems with unstable dynamics at both the direct and recycling paths as well as different time delays for each path. The main contribution of this work is to provide a stabilizing strategy of such class of systems using an observer-based control approach. Stability results concerning stable recycling systems or partially unstable recycling system can be found in literature. However, to the best of our knowledge, there are no stability results when unstable dynamics are considered in both paths of the recycling process. Necessary and sufficient stability conditions of the proposed stabilizing controllers are obtained from a frequency domain analysis.