Contractibility of overlapping decentralized control

The purpose of the paper is to generalize the concept of contractibility of decentralized control laws in the inclusion principle. After a system with overlapping subsystems is expanded into a larger space, and decentralized control laws are formulated for the disjoint subsystems, the laws need to be contracted for implementation in the original space. We propose broader definitions of restriction and aggregation in the framework of inclusion, which provide more flexibility in the contraction phase of the expansion-contraction process. In particular, we discuss contractibility conditions for dynamic output controllers including state observers which have been of special interest in applications.