Resilient H−/H∞ Fault Detection for Uncertain Switched Singular Systems With Mode‐Dependent Persistent Dwell Time

ABSTRACT This study addresses the issue of resilient fault detection for discrete‐time uncertain switched singular systems (SSSs). The type of mode‐dependent persistent dwell time (MDPDT) switching is exploited due to its enhanced practical applicability over the conventional mode‐dependent average dwell time switching. Within the framework of mixed performance indices, we develop a novel design methodology for resilient fault detection observers (FDOs) of SSSs. The research proceeds through the following key stages. First, we establish a criterion of admissibility for SSSs with MDPDT. Second, we derive existence conditions of resilient and FDOs for uncertain SSSs, respectively. Next, we formulate the resilient FDO synthesis as an optimization problem to the ratio of the two performance indices, and propose an innovative algorithm to achieve a compromise between the robustness against disturbances and the sensitivity to faults. Finally, the effectiveness and advantages of the proposed resilient FDO design method are validated using an illustrative example by comparing it with the non‐resilient case.