It is well known that the Popov stability criterion is equivalent to the existence of a Lyapunov function of the Lur’e-Postnikov form. In this paper, this idea is extended to the problem of output feedback robust stabilization. The paper defines a notion of ’absolute stabilization with a Lyapunov function of the Lur’e-Postnikov form’. The main result is a necessary and sufficient condition for this property. This condition is given in terms of the existence of suitable solutions to a pair of algebraic Riccati equations.