  Goal-driven selective attention (GDSA) is a remarkable function that allows
the complex dynamical networks of the brain to support coherent perception and
cognition. Part I of this two-part paper proposes a new control-theoretic
framework, termed hierarchical selective recruitment (HSR), to rigorously
explain the emergence of GDSA from the brain's network structure and dynamics.
This part completes the development of HSR by deriving conditions on the joint
structure of the hierarchical subnetworks that guarantee top-down recruitment
of the task-relevant part of each subnetwork by the subnetwork at the layer
immediately above, while inhibiting the activity of task-irrelevant subnetworks
at all the hierarchical layers. To further verify the merit and applicability
of this framework, we carry out a comprehensive case study of selective
listening in rodents and show that a small network with HSR-based structure and
minimal size can explain the data with remarkable accuracy while satisfying the
theoretical requirements of HSR. Our technical approach relies on the theory of
switched systems and provides a novel converse Lyapunov theorem for
state-dependent switched affine systems that is of independent interest.
