In this work, we present a study on the long time-scale period variations of four single-mode high-amplitude delta Scuti stars (HADS) via the classical $O-C$ analysis. The target HADS are (i) XX Cygni, (ii) YZ Bootis, (iii) GP Andromedae, and (iv) ZZ Microscopii. The newly determined times of maximum light came from the Transiting Exoplanet Survey Satellite (TESS), American Association of Variable Star Observers (AAVSO), and Bundesdeutsche Arbeitsgemeinschaft f$\ddot{\rm u}$r Ver$\ddot{\rm a}$nderliche Sterne (BAV) projects. Together with the times of maximum light obtained in the historical literature, the $O-C$ analysis was performed on these HADS, in which we obtained the linear period variation rates $\dot{P}/P$ as $(9.2 \pm 0.2) \times 10^{-9} \ \mathrm{yr^{-1}}$, $(3.2\pm 0.2)\times 10^{-9} \ \mathrm{yr^{-1}}$, $(4.22\pm 0.03) \times 10^{-8} \ \mathrm{yr^{-1}}$, and $(-2.06 \pm 0.02) \times 10^{-8} \ \mathrm{yr^{-1}}$, respectively. Based on these results and some earlier research, we also discuss the evolutionary stages and the mechanisms of the period variation of these four HADS.
Comment: 12 pages, 5 figures, 1 table. Universe published