Closed-form solution for seismic response of adjacent buildings with linear quadratic Gaussian controllers

You Lin Xu, W. S. Zhang

Research output: Journal article publicationJournal articleAcademic researchpeer-review

36 Citations (Scopus)


Closed-form solution for seismic response of adjacent buildings connected by hydraulic actuators with linear quadratic Gaussian (LQG) controllers is presented in this paper. The equations of motion of actively controlled adjacent buildings against earthquake are first established. The complex modal superposition method is then used to determine dynamic characteristics, including modal damping ratio, of actively controlled adjacent buildings. The closed-form solution for seismic response of the system is finally derived in terms of the complex dynamic characteristics, the pseudo-excitation method and the residue theorem. By using the closed-form solution, extensive parametric studies can be carried out for the system of many degrees of freedom. The beneficial parameters of LQG controllers for achieving the maximum response reduction of both buildings using reasonable control forces can be identified. The effectiveness of LQG controllers for this particular application is evaluated in this study. The results show that for the adjacent buildings of different dynamic properties, if the parameters of LQG controllers are selected appropriately, the modal damping ratios of the system can be significantly increased and the seismic responses of both buildings can be considerably reduced.
Original languageEnglish
Pages (from-to)235-259
Number of pages25
JournalEarthquake Engineering and Structural Dynamics
Issue number2
Publication statusPublished - 1 Jan 2002


  • Adjacent building
  • Closed-form solution
  • LQG controller
  • Parametric study
  • Seismic response

ASJC Scopus subject areas

  • Geotechnical Engineering and Engineering Geology
  • Earth and Planetary Sciences (miscellaneous)

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