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Matrix converters have no boost capabilities. Their output voltage amplitude is therefore reduced compared to back-to-back inverter topologies. Moreover, they are sensitive to grid voltage fluctuations and disturbances and the voltage transfer ratio is further reduced under such grid perturbations. The present paper analyses the behaviour and limits of the two-stage matrix converters. It proposes and investigates three alternative topologies that modify the DC-link voltage of the two-stage matrix converter, by the means of additional circuitry, in order to increase the voltage transfer ratio above unity and to obtain immunity to grid disturbances. A high-performance control of the grid current is required to obtain a power factor close to unity. An effective control method is proposed for each converter. Feedforward model predictive controllers allow obtaining good performances. The performances of the topologies are finally analysed and compared.