Observer-based fault detection scheme for a class of discrete time-delay systems

In this contribution, robust fault detection problems for discrete time-delay systems with l
2
-norm bounded unknown inputs are studied. The basic idea of our study is first to introduce a state-memoryless observer-based fault detection filter (FDF) as the residual generator and then to formulate such a FDF design problem as an H
∞
optimization problem in the sense of increasing the sensitivity of residual to the faults, while simultaneously enhancing the robustness of residual to unknown input as well as plant input. The main results consist of the formulation of such a residual generation optimization problem, solvability conditions and the derivation of an analytic solution. The residual evaluation problem is also considered, which includes the determination of residual evaluation function and threshold. A numerical example is used to demonstrate the proposed fault detection scheme.