Towards quantitative time domain design tradeoffs in nonlinear control

This paper analyzes the feasibility of quantifying design tradeoffs on the transient step response of a class of nonlinear systems. This feasibility analysis builds on available tools for the characterization of performance limitations in the optimal quadratic response of the class of strict feedback nonlinear systems. We present results that show that, as in linear systems, for certain classes of nonminimum, phase systems, the closed loop transient step response must display undershoot. A lower bound on this undershoot can be computed based on the settling time of the system, and this bound increases as the settling time is decreased.