Quadratic separators in the input-output setting

The paper provides a formulation of the quadratic separator result in a fairly general input-output operator framework and it focuses on the specific points that are different compared to the usual finite dimensional formulations. The major contribution of the paper is to emphasize the role of the causality in obtaining the stability result having a quadratic separator and the fact that the plant and the boundedness constant in the formulation of the well-posedness condition determine the robust stability domain associated to the given plant, i.e., the set of those systems {K} that stabilizes the given plant and produce the given “disturbance rejection” level γ Concerning the causality issue the necessity of the homotopy argument in the IQC results is also explained and its relation with a general result concerning nest algebras is pointed out.