Estimating the performance of approximately feedback linearized systems

A method for estimating the performance of approximately feedback linearized systems is presented. The objective is to quantify the interactions among three important performance measures: the aggressiveness of the desired trajectory, the tracking error, and the domain of attraction. The proposed approach begins with the formulation of an optimization problem based on Lyapunov theory. Solving this optimization problem makes it possible to construct a nonsmooth solution manifold that characterizes the system performance. Nonsmooth analysis is used to analyze the important functions involved in the optimization and to develop a path-following algorithm for calculating the desired manifold.<>