<p>This paper investigates the problem of rate bumpless transfer fault detection (BTFD) filtering for switched systems composed entirely of unstable subsystems. To alleviate abrupt and significant fluctuations in the fault detection filter (FDF) rate signals during switching events, we propose a novel rate bumpless transfer (BT) performance criterion. Additionally, a generalized concept of mode-dependent interval dwell time (MDIDT) is introduced to guarantee the stability of switched systems, extending the conventional notion of dwell time switching. Our primary objective is to design an effective FDF that ensures asymptotic stability of the augmented system under MDIDT switching conditions, while simultaneously satisfying weighted <i>H</i>_∞ performance and rate bumpless transfer requirements. By employing a discretized Lyapunov function approach, we derive sufficient conditions to address the rate BTFD filtering challenge. Finally, a numerical example demonstrates the effectiveness and advantages of the proposed approach.</p>