Confidence ellipsoids for uncertain linear equations with structure

In this paper we show how to compute, via semidefinite programming, ellipsoids of confidence for linear equations with structured (unknown-but-bounded) perturbations. Our results are exact in the "unstructured" perturbations case, enabling us to recover in particular the classical case when the perturbation is additive. The approach can be used for example in the identification of structured, dynamical systems.