A cascaded H-bridge based pulse generator for transcranial magnetic stimulation is introduced. The system demonstrates complete flexibility for producing different shape, duration, direction, and rate of repetition of stimulus pulses within its electrical limits, and can emulate all commercial and research systems available to-date in this application space. An offline model predictive control algorithm, used to generate pulses and sequences, shows superior performance compared to conventional carrier-based pulse width modulation. A fully functioning laboratory prototype delivers up to 1.5 kV, 6 kA pulses, and is ready to be used as a research tool for the exploration of transcranial magnetic stimulation therapies by leveraging the many degrees-of-freedom offered by the design.