Robust finite frequency H∞H∞ static-output-feedback control with application to vibration active control of structural systems

In this work, the robust finite frequency H∞H∞ passive fault-tolerant static-output-feedback controller design problem is investigated. The control law is a static-output-feedback control and the actuators are subject to faults. The fault matrix is described by a polytope with finite vertices. In order to attenuate the effect from the external disturbance to the controlled output, the finite frequency H∞H∞ control is employed and the Hamilton matrix is avoided. The static-output-feedback gain is determined via a two-stage method. Then, an iterative algorithm is proposed to derive a minimum H∞H∞ performance index. The proposed algorithm is applied to an active control problem of a structural system under an earthquake excitation. Simulations and comparisons have shown that the designed fault-tolerant controller can significantly attenuate the vibration from the ground and protect the structural system even actuator faults occur.