Absolute stability of 2nd order discrete-time single variable lur'e systems

In this paper the absolute stability of 2nd order discrete-time single variable Lur'e systems is investigated. Simple sufficient conditions for the existence of a common unic Lyapunov function are presented. A necessary condition for the existence of a common unic Liapunov function for 2nd order discrete Lur'e systems is expressed as a simple restriction on the root locus of the system.