Data-driven fault detection filter design for time-delay systems

In this paper, robust fault detection (FD) problems for time-delay LTI systems with unknown inputs are studied. This paper is proposed to evaluate the robustness as well as sensitivity of residual signals to the unknown inputs as well as to the faults in terms of L₂. First, the weighting matrix is selected for an appropriate design of filter, then fault detection filter design with Lyapunov-Krasovskii function (LKF) is designed with time delay. The main results include the detailed derivation of these steps followed by its implementation on an open-loop time-delay system for chemical reactor example.