About the Kalman-Yakubovich-Popov Lemma and non-minimal state-space realizations

Abstract

This paper is devoted to the implications of the Kalman-Yakubovich-Popov Lemma, or Positive Real Lemma, when non-minimal state space realizations of transfer matrices of linear continuous systems are used. It is seen that some spurious parametrical conditions on the transfer matrix keep the Positive Real Lemma guaranteeing the stability from the associated Lyapunov equation.