The dead-beat UIO assumption, while simplifying the fault detection and identification process, may have limitations in certain scenarios. One potential limitation is the assumption of perfect state estimation, which may not always be achievable in practical systems due to modeling errors, noise, or uncertainties. To address this limitation, the approach could be adapted to work with asymptotic UIOs, which provide a more robust estimation of the system states over time. By incorporating asymptotic UIOs, the system can account for estimation errors and uncertainties, leading to more reliable fault detection and identification. This adaptation would involve adjusting the fault identification algorithm to accommodate the estimation error and ensure accurate fault isolation even in the presence of uncertainties.