RFDF design for linear time-delay systems with unknown inputs and parameter uncertainties

Abstract

The robust fault detection filter (RFDF) design problems are studied for linear time-delay systems with both unknown inputs and parameter uncertainties. Firstly, a reference residual model is introduced to formulate the RFDF design problem as an H _∞ model-matching problem. The reference residual model presented in this article is assumed to be an optimal residual generator without uncertainties, which takes into account the robustness against disturbances and sensitivity to faults simultaneously. Then applying robust H _∞ optimization control technique, the existence conditions of the RFDF for linear uncertain time-delay systems are presented in terms of linear matrix inequality (LMI) formulation, independently of time delay. In order to detect the fault, an adaptive threshold which depends on the inputs and can be calculated on-line is finally determined. An illustrative design example is used to demonstrate the validity and applicability of the proposed approach.

Keywords:

• Time-delay systems
• Robust fault detection filter (RFDF)
• Model matching
• H _∞ optimization
• Linear matrix inequality (LMI)

Acknowledgments

The authors would like to thank the anonymous referees and the editor for their constructive and valuable comments that have improved the presentation.