The Zames-Falb IQC for critically stable systems

A feedback interconnection of a neutrally stable linear time-invariant system and a nonlinearity with 0/spl les/ x/spl phi/(x)/spl les/kx/sup 2/ is called critical since the worst case linearization is at best neutrally stable. This makes the stability analysis of such systems particularly hard. It will be shown that an integrator and a sector bounded nonlinearity can be encapsulated in a bounded operator that satisfies several useful integral quadratic constraints. This gives powerful tools for stability analysis of critically stable systems.