An LMI approach to design robust fault detection filter for uncertain Lur’e singularly perturbed systems

In this paper, the robust fault detection filter (RFDF) design problem for uncertain Lur’e singularly perturbed systems (SPSs) with unknown inputs is studied. Firstly, an optimal residual generator is constructed as a reference model, and the design of the RFDF for the system is formulated as an $H_{\infty}$ model matching problem. Secondly, based on the linear matrix inequality (LMI) theory, the sufficient conditions for the augmented system to be absolutely stable and satisfy the $H_{\infty}$ performance index are derived. Then an algorithm is proposed to solve the optimization problem, based on this, the specific parameters of the RFDF are obtained by using the LMI toolbox, and the fault detection method based on residual signal is obtained. Finally, a numerical example is given to verify the feasibility and effectiveness of the proposed results.