An optimal design approach to mixed H_ /H∞ fault detection system

An optimal design approach to fault detection with H_ index and H_infin norm for linear time invariant systems is proposed. At first a linear full-order observer is constructed and the dynamics of residual generator which involves unknown inputs represented by disturbances, noise, model uncertainty and faults is acquired. The sensitivity of residual to faults is characterized by H_ index, and the robustness of residual to unknown inputs is denoted by H_infin norm respectively. By using linear matrix inequality (LMI) method, the existence condition of mixed H_/H_infin fault detection observer gain and its solving approach is derived, which leads to an iterative algorithm for optimal solution. Finally the optimal fault detection system can be achieved with maximal sensitivity to faults and robustness against unknown inputs simultaneously. A numerical example is employed to illustrate the effectiveness of the present approach.