  We propose a scheme for controlling nonlinear coherent perfect absorption
(CPA) in a three-level \Lambda-type atom-cavity system. Generally, the normally
nonlinear CPA and the bistable CPA can be attained at the different frequencies
of an input probe field. With a coherent control field coupling one of the
ground states and the excited state of the atoms, two types of CPA can be
attained at the same frequency. Besides, for the bistable CPA, the highest
output-input ratio of the high stable state and the low stable state is
approximately 1, and the bistable region is controllable with the control
field. The controllable bistable CPA may have potential applications in optical
bistable switching and optical logic devices
