Fault detection filter design for LTI system with time delays

This paper deals with the fault detection filter design problem for linear time invariant time-delay systems with unknown input. The core of our study is to a) take the behavior of delayed state and measurement into consideration when the observer-based fault detection filter is constructed; b) solve the formulated fault detection filter design problem by combining of using the left eigenstructure assignment approach and H_∞ optimization technique. Through a suitable choice of the filter gain matrices and residual weighting matrix, the residual can be completely decoupled from the delay-free unknown input, while the influence of the delayed unknown input on residual is minimized in the sense of H_∞ norm. Numerical simulation is used to illustrate the efficiency of the proposed method.