Optimal diagnostic observer for sampled-data systems

The direct design method of optimal diagnostic observer for sampled-data systems is investigated in this paper. Firstly, an appropriate diagnostic observer for sampled-data systems is constructed from the transfer function viewpoint and the dynamics of the discrete time residual with respect to continuous time unknown inputs and faults is derived. Then, the sampled-data fault detection problem is formulated as a class of ratio-type optimization one. By using the co-inner-outer factorization technique and algebra method, a general optimal solution is obtained to make the discrete-time residual robust to the continuous-time unknown inputs and sensitive to the faults. Finally, simulation results of a numerical example are provided to illustrate the efficiency of the proposed method.