Robust fault detection dynamic observer design for LTI systems

Dynamic observer provides more freedom to meet the diversified performance specifications for fault detection purpose in contrast with static observer. However, little attention is paid on its design and only a few papers investigated how to design a fault detection dynamic observer. In this work, we propose an innovative dynamic observer design approach for linear time invariant (LTI) systems subjected to unknown disturbance and possible faults with the aid of the generalized KYP lemma developed recently. The dynamic observer is designed such that the disturbances are attenuated to a specified level to meet the H∞ performance in the concerned finite frequency interval while the sensitivity to the possible faults in its frequency domain is maximized in the H- index sense. The existence conditions of such an observer are given in terms of linear matrix inequalities (LMIs). An iterative algorithm is presented to achieve the solution. The effectiveness of the proposed method is illustrated by a numerical example.