Research ArticleRobust fault detection for switched positive linear systems with time-varying delays

- Positive L1 filtering for the switched positive systems with time-varying delay is proposed.
- Sufficient conditions for the existence of robust fault detection filter design problem are established.
- The designed filter can guarantee the positivity of the observations and the error signals.
- The proposed method can be solved directly by the Matlab LMI toolbox.

This paper investigates the problem of robust fault detection for a class of switched positive linear systems with time-varying delays. The fault detection filter is used as the residual generator, in which the filter parameters are dependent on the system mode. Attention is focused on designing the positive filter such that, for model uncertainties, unknown inputs and the control inputs, the error between the residual and fault is minimized. The problem of robust fault detection is converted into a positive L1 filtering problem. Subsequently, by constructing an appropriate multiple co-positive type Lyapunov-Krasovskii functional, as well as using the average dwell time approach, sufficient conditions for the solvability of this problem are established in terms of linear matrix inequalities (LMIs). Two illustrative examples are provided to show the effectiveness and applicability of the proposed results.