Decentralized Controller Design for Descriptor-type Time-delay Systems Composed of Overlapping Subsystems

Decentralized controller design for descriptor-type time-delay systems, which are composed of a number of overlapping subsystems, is considered. The concepts of inclusion and restriction are first introduced for such systems. Then, using these concepts, the overlapping decompositions and expansion of such systems are presented. Then, decentralized controller design for such a system, using its expansion is presented. Since the subsystems of the expanded system are non-overlapping, it may be easier to design controllers for the expanded system, rather than directly for the original system. It is shown that, decentralized controllers designed for the expanded system can be applied to the original system. Furthermore, if these controllers stabilize the expanded system and achieve desired performance for the expanded system, they also stabilize the original system and achieve desired performance for the original system.