## 1 Introduction
Relevant aspects associated to practical implementations are discussed in [33; 34]. In this paper, we present an advanced computational procedure to design distributed systems of interstory FVDs with high-performance characteristics. The proposed design methodology exploits the connections between systems of distributed interstory FVDs (see Figure 2a) and decentralized static velocity-feedback (SVF) control systems with ideal interstory force-actuation devices and collocated interstory-velocity sensors (see Figure 3a). That approach allows casting the optimal tuning of passive FVD systems as a decentralized static output-feedback (SOF) controller-design problem, which can be formulated as a structured optimization problem with bilinear matrix inequality (BMI) constraints. The BMI optimization problem can later be converted into a structured linear matrix inequality (LMI) optimization problem by means of a suitable transformation of variables, which contains a matrix \(\mathbf{L}\) whose values can be arbitrarily selected to improve the feasibility and effectiveness of the computational method [35; 36]. That line of solution has been applied with positive results to the design of interstory FVD systems and hybrid interstory-interbuilding FVD systems in multibuilding problems [20; 31; 37]. Preliminary works with a null \(L\)-matrix revealed feasibility issues in the LMI optimization problem that were partially solved by introducing a numerical perturbation in the state-space model [35; 37]. Improved feasibility results have been obtained with more advanced \(L\)-matrix choices that use numerical data provided by the optimal state-feedback controller [38]. However, that approach has the computational drawback of requiring the previous design of a full-state feedback controller [20; 31]. Figure 2: Schematic model of a multistory building equipped with a complete set of interstory fluid viscous dampers. The main contribution of the present work is a novel iterative linear matrix inequality (ILMI) procedure that generates a sequence of improved structured SOF controllers by means of a smart choice of the \(L\)-matrices. Compared with previous works [20; 31; 35; 37], the proposed ILMI procedure allows a more effective treatment of the feasibility issues, which are now circumscribed to the initial step and separated from the optimality requirements. The modeling aspects are covered in Section 2, where we examine the connections between systems of interstory FVDs and decentralized SVF active controllers, and provide a state-space model for a multistory building equipped with a system of ideal interstory force-actuation devices and a set of collocated interstory-velocity sensors. The details of the ILMI procedure are discussed in Section 3, where we introduce a suitable LMI formulation for structured SOF \(H_{\infty}\) controllers, provide a formal proof of the correct definition of the iterates, and present a solution for the initialization step. In Section 4, the proposed design methodology is applied to compute the damping constants of a system of interstory FVDs for the seismic protection of a five-story building. For the obtained FVD system, the frequency response function (FRF) characteristics and the time-domain responses produced by the full-scale El Centro 1940 seismic record are studied and compared with the behavior of the optimal static state-feedback \(H_{\infty}\) controller. The results in that section demonstrate the effectiveness of the proposed ILMI procedure and the high-performance characteristics of the designed passive ISSD system.