Fundamental limitations of discrete-time adaptive nonlinear control

A particular polynomial is introduced in this paper which can be used to de termine under what conditions a typical class of discretetime nonlinear sys tems with uncertainties in both parameters and noises is not stabilizable b y feedback, thus demonstrating the fundamental limitations of discrete-time adaptive nonlinear control. As a consequence, it is shown that for nonline ar systems with unknown parameters and noises, the systems may indeed be no nstabilizable, in general, whenever the usual linear growth condition is re laxed and the number of unknown parameters is large, even though the corres ponding noise-free systems are globally stabilizable.