Fundamental limitations of discrete-time adaptive nonlinear control

A particular polynomial is introduced in this paper which can be used to determine under what conditions a typical class of discretetime nonlinear systems with uncertainties in both parameters and noises is not stabilizable by feedback, thus demonstrating the fundamental limitations of discrete-time adaptive nonlinear control. As a consequence, it is shown that for nonlinear systems with unknown parameters and noises, the systems may indeed be nonstabilizable, in general, whenever the usual linear growth condition is relaxed and the number of unknown parameters is large, even though the corresponding noise-free systems are globally stabilizable.