Elimination lemma and contractive extensions

The Elimination lemma provides analysis conditions that constitute a fundamental tool in obtaining state space solutions of robust control design problems. Using operator theoretical concepts, the paper provides a derivation of the Elimination lemma based on a contractive extension principle and to give a Krein space geometric interpretation of the result. In this way the statement of the lemma is related to general techniques, like interpolation and commutant lifting theory. This result is considered to be an initial step in the control relevant formulation of the lemma in an infinite dimensional setting.