Fault Detection for Switched Positive Systems by Zonotope‐Based Dynamic Residual Evaluation Approach

ABSTRACT This research investigates the fault detection for discrete‐time switched positive systems under unknown‐but‐bounded disturbances through a zonotope‐based residual evaluation methodology. Compared with the existing findings, the proposed framework introduces a dynamic threshold, thereby achieving an improvement in detection sensitivity while preserving robustness against disturbances. First, we develop a criterion to guarantee the stability and performance for the augmented system. Building upon the analysis results, a co‐design procedure is formulated to simultaneously optimize positive fault detection observers and switching signals for the underlying system. Furthermore, we construct a residual zonotope that geometrically encapsulates the admissible state trajectories of the fault‐free augmented system. The efficacy of the presented zonotopic fault detection scheme is substantiated through illustrative examples.