An illumination system (1) comprises a plurality of light source assemblies (10) and a common controller (21). Each light source assembly (10) comprises a plurality of individually controllable light sources (11, 12, 13) for generating light of mutually different colors. The controller is designed to generate a plurality of switched frequency signals (SF1, SF2, SF3) for the respective light sources, with a frequency within a relatively small frequency band, the different frequency signals (SF1, SF2, SF3) having mutually different frequencies (f1, f2, f3). In each light source assembly, each light source is responsive to a respective one of said switched frequency signals (SF1, SF2, SF3), the light source being ON for as long as the respective switched frequency signal is zero and being OFF for as long as the respective switched frequency signal has the respective frequency.