Sequential design of multi-overlapping controllers for longitudinal multi-overlapping systems Francisco Palacios-Qui˜ nonero a , Jos´ e Rodellar b , Josep M. Rossell a a Department of Applied Mathematics III, Universitat Polit` ecnica de Catalunya (UPC), 08240-Manresa, Spain b Department of Applied Mathematics III, Universitat Polit` ecnica de Catalunya (UPC), Campus Nord, C-2, 08034-Barcelona Abstract 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. Key words: Inclusion principle, multi-overlapping decomposition, information structure constraints, decentralized control, building structures. 1 Introduction Dimensionality, uncertainty, and information constraints are fundamental char- acteristics of system complexity [9]. When a complex system can be decom- posed into disjoint subsystems, a set of local controllers may be independently Email addresses: francisco.palacios@upc.edu (Francisco Palacios-Qui˜ nonero), jose.rodellar@upc.edu (Jos´ e Rodellar), josep.maria.rossell@upc.edu (Josep M. Rossell). 1 This work was supported in part by the Spanish Committee for Science and Technology (CICYT) under Grant DPI2008-06699-C02-02 and DPI2008-06564-C02- 02 Preprint submitted to AMC 30 April 2010