  This paper studies the identification of linear time-invariant systems using
noisy input-output data in a set-membership framework. It is assumed that the
noise sequence belongs to a bounded set, induced by a quadratic matrix
inequality, that allows for capturing various energy-bounded noise models. In
this framework, the identification problem is to find an estimation for the
true system so that the worst-case estimation error with respect to a given
norm is minimized. For such a problem, we present closed-form solutions with
respect to arbitrary unitarily invariant matrix norms. Examples of these norms
include the Frobenius norm, spectral norm, nuclear norm, Schatten p-norms, and
Ky Fan k-norms.
