Fault detection in uncertain linear continuous-time periodic systems

This paper studies fault detection problem of linear continuous-time periodic systems. At first, an optimal periodic observer-based residual generator is derived for the case of no model uncertainty, which achieves the best compromise between the sensitivity to faults and the robustness to unknown disturbances. Then, in order to deal with model uncertainty, a post-filter is introduced which provides more design freedom and the residual generator is designed to approximate the best compromise character. Periodic Riccati differential equation and periodic differential LMI play an important role in the computation of the optimal solution.