  Recent control trends are increasingly relying on communication networks and
wireless channels to close the loop for Internet-of-Things applications.
Traditionally these approaches are model-based, i.e., assuming a network or
channel model they are focused on stability analysis and appropriate controller
designs. However the availability of such wireless channel modeling is
fundamentally challenging in practice as channels are typically unknown a
priori and only available through data samples. In this work we aim to develop
algorithms that rely on channel sample data to determine the stability and
performance of networked control tasks. In this regard our work is the first to
characterize the amount of channel modeling that is required to answer such a
question. Specifically we examine how many channel data samples are required in
order to answer with high confidence whether a given networked control system
is stable or not. This analysis is based on the notion of sample complexity
from the learning literature and is facilitated by concentration inequalities.
Moreover we establish a direct relation between the sample complexity and the
networked system stability margin, i.e., the underlying packet success rate of
the channel and the spectral radius of the dynamics of the control system. This
illustrates that it becomes impractical to verify stability under a large range
of plant and channel configurations. We validate our theoretical results in
numerical simulations.
