Design of robust fault detection in uncertain linear systems via high-order PI observers

The problem of designing robust fault detection via high-order proportional integral (PI) observers in uncertain linear systems with disturbances is investigated. Based on the parametric solutions of a class of Sylvester matrix equations, the problem of designing robust fault detection via high-order PI observers is changed into an optimal problem with multiple constraints. Based on the solution of the optimal problem, the necessary and sufficient existence condition of the high-order PI observer with the robust fault detection function is derived, and a design method of robust fault detection in uncertain linear systems with disturbances is proposed. Finally, a numerical example and its simulation results show that the proposed method is effective.