A novel dimming control scheme, termed as generalized dimming control (GDC), is proposed for visible light communication (VLC) systems. The proposed GDC scheme achieves dimming control by simultaneously adjusting the intensity of transmitted symbols and the number of active elements in a space-time matrix. Both the indices of the active elements in each space-time matrix and the modulated constellation symbols are used to carry information. Since illumination is deemed as the prior task of VLC, an incremental algorithm for index mapping is proposed for achieving target optical power and uniform illumination. Next, GDC having the optimal activation pattern is investigated to further improve the bit-error rate (BER) performance. In particular, the BER performance of GDC is analyzed using the union bound technique. Based on the analytical BER bound, the optimal activation pattern of GDC scheme with the minimum BER criterion (GDC-MBER) is obtained by exhaustively searching all conditional pairwise error probabilities. However, since GDC-MBER requires high search complexity, two low-complexity GDC schemes having the maximum free distance criterion (GDCMFD) are proposed. The first GDC-MFD scheme, coined as GDC-MFD1, reduces the computational complexity by deriving a lower bound of the free distance based on Rayleigh-Ritz theorem. Based on the time-invariance characteristics of the VLC channel, GDC-MFD2 is proposed to further reduce the required computation efforts. Simulation and numerical results show that GDC-MBER, GDC-MFD1 and GDC-MFD2 have similar BER performance, and they can achieve 2 dB performance gains over conventional hybrid dimming control scheme and 7 dB performance gains over digital dimming control schemes.