<p>The inverter system supplying a memristive load exhibits strong nonlinearity, is prone to various instabilities and leads to elevated system harmonics, thus investigating its instability mechanism is critical to ensure stable system operation. In this paper, the interesting continuous changing multiple bifurcations on scale of switching cycle in single-phase T-type three-level inverter supplying memristive load (STTISML) controlled via voltage-equalizing and proportional-integral-derivative (PID) loop is explored. Initially, the state equation of the STTISML is established, whose coefficient matrix is irreversible and periodically time-varying, accordingly the STTISML is a segmented nonlinear smooth periodic time-varying system that is Filippov system. Then, the stroboscopic mapping discrete model of the STTISML is constructed, Filippov method is employed to acquire Monodromy matrix, and Floquet theory is utilized to ascertain operational state of the STTISML. Subsequently, theoretical research discloses that the unstable behaviors on scale of switching cycle in the STTISML arise from strikingly continuous changing occurrence of Period-doubling bifurcation (PDB), instantaneous Hopf bifurcation (HB), and Saddle-node bifurcation (SNB). Additionally, the sensitivities of Floquet exponents for varied system parameters are computed, to assess key parameters influencing the occurrence of multiple bifurcations in the STTISML; the multiple bifurcations boundaries in diverse control and memristive parameters spaces are depicted. Eventually, both PSpice simulations and hardware experiment are performed, also the concordance between simulation results and experimental measurements has validated the precision of theoretical analyses. Findings herein further deepen the understanding of complex bifurcation mechanisms in the STTISML, and provide substantial information for its optimal design and practical stable operation.</p>