Actuator fault estimation based on adaptive H∞ observer technique

In adaptive observer methods for actuator fault estimation, the system has to satisfy the condition of the Strictly Positive Realness (SPR). However, some practical systems may fail to satisfy the SPR condition. This paper proposes two methods for actuator fault estimation without the need of the SPR condition, based on the adaptive observer technique with the same structure. At first, for a class of linear time invariant systems without external disturbance, an adaptive fault estimation observer is designed by integrating the output errors. Then, for a class of linear time invariant systems subjected to external disturbance, the fault estimation method based on an adaptive H
_∞
observer is proposed. The observer gain is obtained by solving a linear matrix inequality. The gains of both observers are independent of the sensor fault distribution matrix. The convergence and the existence condition of the designed adaptive observers are analyzed. An example is given to demonstrate the effectiveness of the proposed methods.