A necessary and sufficient condition for high-frequency robustness of non-strictly-proper feedback systems

The author considers stability and robustness of feedback systems, where plant and compensator need not be strictly proper. In his earlier paper (2001) he described a functional R_∞ which, when negative, guarantees closed-loop instability as a result of parasitic interactions in the feedback loop. In his main result, Theorem 5, he proves that, when R_∞>0. there exist perturbations of plant and compensator from a narrow class which result in closed-loop stability and convergence. Hence, one may view R_∞>0 as a necessary and sufficient condition for closed-loop robustness in non-strictly-proper feedback loops