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By introducing a feedback path in the conventional droop control loop of islanded microgrid, the voltage amplitude and frequency restoration can be effectively achieved by using the secondary control. However, the usage of low bandwidth communication (LBC) links, the communication delays and the underlying data drop, would increase the system complexity and reduce its reliability. In our previous studies, it is found that the voltage and frequency deviation of islanded three-phase microgrid in synchronous reference frame can be restored by utilizing a band-pass filter (BPF)-based improved droop control strategy, without any communication lines and additional control loops. For more general scenarios, the BPF-based droop control scheme is first extended to islanded single-phase microgrid in hybrid frame in this paper to achieve deviation restoration. Moreover, the dynamic stability of the studied system is addressed by the derived reduced-order small-signal model in this paper, which simplify the modeling process and theoretical analysis. Followed by the system model, the impact of system parameters variation on the stability and dynamic performance of the microgrid are subsequently predicted by applying the eigenvalue-based analysis approach. Consequently, the analytical results show an overdamped system with good stability and robustness against system parameters drift. Finally, the effectiveness of eigenvalue analysis is verified by simulation results, and the experiment results are provided to further validate the feasibility of BPF-based droop control method in islanded single-phase microgrid.