  We show that long-distance steady-state quantum correlations (entanglement)
between pairs of cavity-atom systems in an array of lossy and driven coupled
resonators can be established and controlled. The maximal of entanglement for
any pair is achieved when their corresponding direct coupling is much smaller
than their individual couplings to the third party. This effect is reminiscent
of the coherent trapping of the $\Lambda-$type three-level atoms using two
classical coherent fields. Different geometries for coherent control are
considered. For finite temperature, the steady state of the coupled lossy
atom-cavity arrays with driving fields is in general not a thermal state. Using
an appropriate distance measure for quantum states, we find that the change
rate of the degree of thermalization with respect to the driving strength is
consistent with the entanglement of the system.
