A Novel Iterative Linear Matrix Inequality Design Procedure for Passive Inter-Substructure Vibration Control

In vibration control of compound structures, inter-substructure damper (ISSD) systems exploit the out-of-phase response of different substructures to dissipate the kinetic vibrational energy by means of inter-substructure damping links. For seismic protection of multistory buildings, distributed sets of interstory fluid viscous dampers (FVDs) are ISSD systems of particular interest. The connections between distributed FVD systems and decentralized static output-feedback control allow using advanced controller-design methodologies to obtain passive ISSD systems with high-performance characteristics. A major issue of that approach is the computational difficulties associated to the numerical solution of optimization problems with structured bilinear matrix inequality constraints. In this work, we present a novel iterative linear matrix inequality procedure that can be applied to obtain enhanced suboptimal solutions for that kind of optimization problems. To demonstrate the effectiveness of the proposed methodology, we design a system of supplementary interstory FVDs for the seismic protection of a five-story building by synthesizing a decentralized static velocity-feedback H∞ controller. In the performance assessment, we compare the frequency-domain and time-domain responses of the designed FVD system with the behavior of the optimal static state-feedback H∞ controller. The obtained results indicate that the proposed approach allows designing passive ISSD systems that are capable to match the level of performance attained by optimal state-feedback active controllers.

An LMI Approach to Mixed H_/H∞ Robust Fault Detection Observer Design

This paper investigates the problem of the robust fault detection (RFD) observer design for linear uncertain systems with the aid of the H_ index and the H∞ norm, which are used to describe the problem of this observer design as optimization problems. Conditions for the existence of such a fault detection observer are given in terms of matrix inequalities. RFD problem with structured uncertainties in the system matrices is also considered. The solution is obtained by an iterative linear matrix inequality (ILMI) algorithm. Numerical example is employed to demonstrate the effectiveness of the proposed methods.

Analysis of Leveling Control System via Iterative Linear Matrix Inequalities with Full Order Observer

This paper investigates leveling control system of suspended access platform using an observer-based controller. Uncertain linear systems for leveling control are derived and represented in terms of a set of matrix inequalities. In the system, all state variables needn’t be measured; the perturbations of leveling control are assumed to be described by structural uncertainties. The stiff problem is avoided since the design procedure is independent of the small parameter. The control problem can be effectively solved by the proposed iterative linear matrix inequality approach. The convergence of the algorithms is also studied. Furthermore, a numerical example and simulation results are given to illustrate the effectiveness of proposed method.