Proportional-Integral Controllers for Minimum-Phase Nonaffine-in-Control Systems

We show that stabilizing tracking proportional-integral (PI) controllers can be constructed for minimum-phase nonaffine-in-control systems. The constructed PI controller is an equivalent realization of an approximate dynamic inversion controller. This equivalence holds only for the time response when applied to the unperturbed system. Even when restricted to unperturbed minimum-phase linear time invariant systems, their closed loop robustness properties differ. This shows that in general, properties that do not define the equivalence relation for systems/controllers are not preserved under such equivalence transformations.