Overlapping Decentralized Robust Servomechanism Problem

Overlapping controller design to solve the servo-mechanism problem within the framework of the extension principle is investigated. Presented approach first involves expending the given plant to obtain a larger dimensional plant such that the overlapping parts of the original plant appear as disjoint. Decentralized controllers are then designed for the expanded system to solve the robust decentralized servomechanism problem. In the final phase these controllers are contracted for implementaion on the original plant. In the present paper the conditions under which there exist solutions to the servo-mechanism problems for the original and the expanded systems are investigated. It is also shown that if a solution is found for the expanded system, a solution for the original system can be obtained by simply contracting the former solution.