A state-space revisit to Redheffer's theorem

The celebrated Redheffer's theorem on linear fractional transformations is rederived in this paper using an algebraic state-space approach based on a generalization of the ARE bounded real lemma recently obtained. This state-space derivation is easier to check and more constructive than the original one and is able to reveal interesting connections between the theorem and some system theory concepts such as dissipativity and storage functions. Moreover a flaw in the original proof is discovered and is corrected here.