A note on robust output feedback stabilization of nonlinear nonminimum phase systems

This paper investigates a few issues related to the problem of robust output feedback stabilization of nonlinear non-minimimum phase systems. In order to cope with (unstructured) parametric uncertainties we insist on well-known high-gain design principles which, however, are integrated with robust zero-assignment procedures to handle possible unstable zero dynamics. In this respect we propose two possible zero-assignment arguments. The first relies upon an output redesign obtained by means of a "feed-through" compensator. Interestingly enough, we show how existing results on this subject can be cast in terms of the resulting feed-through / high-gain design paradigm. In the second, by drawing inspiration from known results for linear systems which go under the name of {em vibrational-feedback}, the output redesign is achieved by using time-varying periodic controllers. Remarkably, we show how the resulting design framework is able to deal also with severe uncertainties in the high-frequency gain of the controlled system by thus obtaining results which turn out to be interesting also in a linear setting.