Robust fault detection filter design for a class of time-delay systems via equivalent transformation

This paper is concerned with the robust fault detection filter (RFDF) design for a class of linear time-invariant systems (LTISs) with output state time delays. Although existing results in literatures study the RFDF for time-delay systems, few is concerned with the output state time-delay systems. The basic idea of our study is to eliminate the time delays of system and transform it to a delay-free system (i.e., a linear time-invariant system without time delays) by the bicausal change of coordinates approach. Then, we design the RFDF for the delay-free LTIS, which is equivalent to the original system with time delays. We first introduce a class of systems with output state time delays, whose fault can be detected by using the RFDF design approach for delay-free systems. Then, since the RFDF design problem can be formulated as a standard H-infinity-model matching problem, it is solved by using H-infinity-optimization LMI techniques. In the last, the adaptive threshold of fault detection is chosen and an illustrative design example is used to demonstrate the validity of the design approach.