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The plasma produced by a pulsed generator is an efficient tool for an airflow control. In this paper, a nanosecond pulsed generator constructed with a fast solid-state switch is designed for triggering synchronous discharges in plasma synthetic jet (PSJ) actuators connected in series. The generator delivers high-voltage pulses with a peak voltage varying from 0 to 20 kV, a rise time of 20 ns, a full-width at half-maximum of 200 ns, and a wide range of pulse-repetition rate varying from 0 to 5.5 kHz. It is proved that this generator is able to trigger synchronous discharges in three PSJ actuators in atmospheric air with a peak discharge current more than 90 A and a deposited energy per pulse of 39 mJ. A schlieren system is used to observe the airflow dynamics, which shows the high synchronization among the three PSJ actuators with a time triggering delay of about 20 ns. The synchronous operation of three PSJ actuators produces a plasma jet with a maximum velocity of 60 m/s and a precursor wave with a velocity of 350 m/s. [ABSTRACT FROM AUTHOR]