Sequential design of multi-overlapping controllers for longitudinal multi-overlapping systems

In this paper a strategy to design multi-overlapping controllers for systems with longitudinal multi-overlapping structure is presented. The design process uses the inclusion principle to carry out a multi-step expansion that allows the decentralized design of a sequence of expanded local controllers. These expanded local controllers are subsequently contracted to produce a multi-overlapping controller that can be implemented in the original system. To illustrate the proposed methodology, the response of a four-story building under a seismic excitation is considered.