For a class of uncertain systems we analyze passification-based adaptive controller in the presence of small, unavoidable input and output time-varying delays as may be present in controller implementation. We derive upper bounds for time delays such that in some domain of initial conditions the states of the closed-loop system tend to zero, whereas an adaptive controller gain tends to a constant value. The results are semi-global, that is the domain of initial conditions is bounded but can be made arbitrary large by tuning an appropriate controller parameter. For the first time, we apply an adaptive controller to linear uncertain networked control systems, where sensors, controllers, and actuators exchange their information through communication networks. The efficiency of the results is demonstrated by the example of adaptive network-based control of an aircraft.