  We introduce a versatile framework to model and study networked control
systems (NCSs). An NCS is described as a feedback interconnection of a plant
and a controller communicating through a bidirectional channel modelled by
cascaded nonlinear two-port networks. This model is sufficiently rich to
capture various properties of a real-world communication channel, such as
distortion, interference, and nonlinearity. Uncertainties in the plant,
controller and communication channels can be handled simultaneously in the
framework. We provide a necessary and sufficient condition for the robust
finite-gain stability of an NCS when the model uncertainties in the plant and
controller are measured by the gap metric and those in the nonlinear
communication channels are measured by operator norms of the uncertain
elements. This condition is given by an inequality involving "arcsine" of the
uncertainty bounds and is derived from novel geometric insights underlying the
robustness of a standard closed-loop system in the presence of conelike
nonlinear perturbations on the system graphs.
