An absolute stability criterion for the Lur'e problem with sector and slope restricted nonlinearities

In this brief we present a new sufficient condition for global asymptotic stability of Lur'e systems with sector and slope restricted nonlinearities. It is expressed as a matrix inequality and is based on an extended Lur'e-Postnikov Lyapunov function. It is compared based on numerical examples to conditions of Josselson-Raju and Haddad-Kapila.