Robust Finite Frequency ℋ∞ Passive Fault Tolerant Static Output Feedback Control with Application to Active Vibration Attenuation

In this work, the robust finite frequency 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∞ control in which the Hamilton matrix is avoided is employed. The static output feedback gain is determined via a two-stage method. Then, an iterative algorithm is proposed to derive a smaller 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.