The Zames-Falb IQC for systems with integrators

A feedback interconnection of a neutrally stable, linear time-invariant sys tem and a nonlinearity with 0 less than or equal to x phi(x) less than or e qual to kx(2) is called critical because the worst case linearization is at best neutrally stable. This characteristic 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, which gives powerf ul tools for stability analysis of a general class of critically stable sys tems.