A time domain approach to robust fault detection of linear time-varying systems

This paper gives the optimal solutions to several robust fault detection problems such as ℋ−/ℋ∞ℋ−/ℋ∞, ℋ2/ℋ∞ℋ2/ℋ∞ and ℋ∞/ℋ∞ℋ∞/ℋ∞ problems for linear time-varying systems in a time domain, which extends the previous results on linear time-invariant systems in a frequency domain. It is shown that all three problems have the same optimal detection filter and the filter is a simple observer obtained by solving a standard differential Riccati equation. Finally, an example is given to illustrate our results.