A contribution to the contractibility problem for overlapping controllers

In this work, a contribution to the contractibility of decentralized control laws, in the context of the Inclusion Principle, is offered. By means of this principle, an overlapping system can be expanded to another bigger one where the subsystems are considered as disjoint. Under a control criterion, local controllers are designed for each subsystem. After this expansion-design process, the decentralized control laws need to be contracted and implemented in the original system. However, the contractibility conditions are not satisfied by arbitrary local gain matrices. In this paper, an explicit structure for the local gain matrices ensuring contractibility is presented; moreover, the possibility of using different control criteria in accordance with these structures is discussed.