Matrix converters convert a three-phase alternating-current power supply to a power supply of a different peak voltage\ud and frequency, and are an emerging technology in a wide variety of applications. However, they are susceptible to an\ud instability, whose behaviour is examined herein. The desired “steady-state” mode of operation of the matrix converter becomes unstable in a Hopf bifurcation as the output/input voltage transfer ratio, q, is increased through some threshold value, qc. Through weakly nonlinear analysis and direct numerical simulation of an averaged model, we show that this bifurcation is subcritical for typical parameter values, leading to hysteresis in the transition to the oscillatory state: there may thus be undesirable large-amplitude oscillations in the output voltages even when q is below the linear stability threshold\ud value qc
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