Fundamental response in the vibration control of buildings subject to seismic excitation with ATMD

Abstract

The linear quadratic regulator for vibration systems subject to seismic excitations is discussed in his own physical newtonian space as a second-order linear differential system with matrix coefficients. The linear quadratic regulator leads to a fourth-order system and second-order transversality conditions. Those systems are studied with a matrix basis generated by a fundamental matrix solution.

Keywords

• earthquake
• control
• vibrating system
• fundamental matrix solution
• lqr problem