  This paper applies a polynomial optimization based framework towards the
superstabilizing control of an Autoregressive with Exogenous Input (ARX) model
given noisy data observations. The recorded input and output values are
corrupted with L-infinity bounded noise where the bounds are known. This is an
instance of Error in Variables (EIV) in which true internal state of the ARX
system remains unknown. The consistency set of ARX models compatible with noisy
data has a bilinearity between unknown plant parameters and unknown noise
terms. The requirement for a dynamic compensator to superstabilize all
consistent plants is expressed using polynomial nonnegativity constraints, and
solved using sum-of-squares (SOS) methods in a converging hierarchy of
semidefinite programs in increasing size. The computational complexity of this
method may be reduced by applying a Theorem of Alternatives to eliminate the
noise terms. Effectiveness of this method is demonstrated on control of example
ARX models.
