Mixed H−/H∞ dynamic observer design for fault detection

Dynamic observer provides more freedom to meet the diversified specifications in contrast with static observer. However, little attention is paid on its application for fault detection purpose. In this work, we propose an innovative dynamic observer based fault detection method 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 and 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.