A push/pop phenomenon for nonlinear systems

The author investigates performance limitations imposed by nonminimum phase characteristics of a nonlinear time-varying plant. A performance criterion is defined which, in the linear case, is analogous to minimizing the sensitivity over a given frequency band. It is shown that if the nonlinear plant is nonminimum phase, then the frequency-weighted sensitivity cannot be made arbitrarily small while keeping the overall sensitivity bounded. The nonminimum phasedness of the plant is stated in terms of deficiency in its range. These results extend the familiar push/pop phenomenon in sensitivity optimization to a nonlinear time-varying setting