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Shock and Vibration
Volume 20 (2013), Issue 2, Pages 297-308

Actuator Saturation and Control Design for Buildings Structural Systems with Improved Uncertainty Description

Y.C. Ding,1 F.L. Weng,2 and Z.A. Yu2

1School of Resources and Environmental Engineering, Jiangxi University of Science and Technology, Ganzhou, Jiangxi, China
2Faculty of Electrical Engineering and Automation, Jiangxi University of Science and Technology, Ganzhou, Jiangxi, China

Received 27 August 2011; Revised 29 August 2012; Accepted 30 August 2012

Copyright © 2013 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The problem of robustly active vibration control for a class of earthquake-excited structural systems with time-delay and saturation in the control input channel and parameter uncertainties appearing in all the mass, damping and stiffness matrices is concerned in this paper. The objective of the designing controllers is to guarantee the robust stability of the closed-loop system and attenuate the disturbance from earthquake excitation. Firstly, by using the linear combination of some matrices to deal with the system's uncertainties, a new system uncertainties description, namely rank-1 uncertainty description, is presented. Then, by introducing a linear varying parameter, the input saturation model is described as a linear parameter varying model. Furthermore, based on parameter-dependent Lyapunov theory and linear matrix inequality (LMI) technique, the LMIs-based conditions for the closed-loop system to be stable are deduced. By solving those conditions, the controller, considering the actuator saturation, input delay and parameters uncertainties, is obtained. Finally, a three-storey linear building structure under earthquake excitation is considered and simulation results are given to show the effectiveness of the proposed controllers.