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.
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