The Circle Criterion and the Lᵖ Stability of Feedback Systems

It is shown that under certain mild assumptions the circle criterion of Sandberg and Zames implies the Lᵖ stability of a broad class of linear time-varying feedback systems for 1 p ∞. Moreover, it is proved that if the input to the feedback configuration tends to zero then so does the output. The results are extended to the case of certain open-loop unstable systems as well as sector bounded nonlinear feedback gains. Finally it is pointed out that all the results apply to any system whose open-loop transmittance