NECESSARY CONDITIONS FOR ASYMPTOTIC TRACKING IN NONLINEAR-SYSTEMS

In the literature, it has been shown that if a single-input single-out put analytic nonlinear plant 1) has a well-defined relative degree and 2) is minimum-phase, it is possible to achieve asymptotic tracking fo r an open set Of output trajectories containing the origin in C(N) [0, infinity), the space of N-times continuously differentable functions taking values in R. When either of these sufficient conditions is not met, various authors have investigated approximate analytic solutions, discontinuous solutions and solutions for restricted sets of trajecto ries. In this paper, it is shown that conditions 1) and 2) are necessa ry for the existence of an analytic compensator which yields asymptoti c tracking for an open set of output trajectories. Analogous results a re established for multi-input multi-output systems.