We study the ability of human observer to control fixation duration during execution of visual search tasks. We conducted the eye-tracking experiments with natural and synthetic images and found the dependency of fixation duration on difficulty of the task and the lengths of preceding and succeeding saccades. In order to explain it, we developed the novel control model of human eye-movements that incorporates continuous-time decision making, observation and update of belief state. This model is based on Partially Observable Markov Decision Process with delay in observation and saccade execution that accounts for a delay between eye and cortex. We validated the computational model through comparison of statistical properties of simulated and experimental eye-movement trajectories.