We describe a system for controlling very large numbers of power semiconductor switching devices (132) to switch in synchronization. The devices are high power devices, for example carrying hundreds of amps and/or voltages of the order of kilovolts. In outline the system comprises a coordinating control system (110, 120), which communicates with a plurality of switching device controllers (130) to control the devices into a plurality of states including a fully-off state, a saturated-on state, and at least one intermediate state between the fully-off and saturated-on states, synchronizing the devices in the at least one intermediate state during switching.